Faculty of Science and Mathematics / PHYSICS / ANALYSIS I

Course:

ANALYSIS I/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
493	Obavezan	1	7	3+3+0

Programs	PHYSICS
Prerequisites
Aims	The aim of the course is mastering the basics of mathematical analysis: the notion of convergence, practical methods for calculation of limit values, elements of differential calculus and its applications in the graphics drawing functions.
Learning outcomes	After passing this exam, the student should be able to 1. Defines the notion of convergent sequence and successfully use various techniques for finding the limit values and prove the convergence of a sequence. 2. Find limit values of functions and determines intervals of their continuity. 3. Make a graph of basic and complex functions. 4. Determines derivatives of basic and complex functions. 5. Use derivatives and The Mean Value Theorem to solve some practical problems in physics, as well as the maximum and minimum problems.
Lecturer / Teaching assistant	Vladimir Božović and Dušica Slović
Methodology	Lectures, exercises, independent work, and consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Review - notion of a sequence, Arithmetic and Geometric sequence.
I week exercises	Review - notion of a sequence, Arithmetic and Geometric sequence.
II week lectures	The notion of convergence, Convergent sequences - definition and examples
II week exercises	The notion of convergence, Convergent sequences - definition and examples
III week lectures	Properties of convergent sequences, Monotone sequences, Number e as a limit of the seqeunce
III week exercises	Properties of convergent sequences, Monotone sequences, Number e as a limit of the seqeunce
IV week lectures	Some interesting application of sequences - Examples in Physics
IV week exercises	Some interesting application of sequences - Examples in Physics
V week lectures	The nootion of series - series as a sequence, Properties of series
V week exercises	The nootion of series - series as a sequence, Properties of series
VI week lectures	The limit of a function, Calculating limits using the limit laws
VI week exercises	The limit of a function, Calculating limits using the limit laws
VII week lectures	The precise definition of a limit, Continuity
VII week exercises	The precise definition of a limit, Continuity
VIII week lectures	Midterm exam
VIII week exercises	Midterm exam
IX week lectures	Derivatives, The derivative as a function, Derivatives of elementary functions
IX week exercises	Derivatives, The derivative as a function, Derivatives of elementary functions
X week lectures	The Chain Rule, Derivatives of functions in implicit and parametric form
X week exercises	The Chain Rule, Derivatives of functions in implicit and parametric form
XI week lectures	Applications of differentiation, Maximum and minimum values, The Mean Value Theorem
XI week exercises	Applications of differentiation, Maximum and minimum values, The Mean Value Theorem
XII week lectures	How derivatives affect the shape of a graph, Indeterminate forms and L’Hospital’s rule, Review
XII week exercises	How derivatives affect the shape of a graph, Indeterminate forms and L’Hospital’s rule, Review
XIII week lectures	Taylor and Maclaurin Series
XIII week exercises	Taylor and Maclaurin Series
XIV week lectures	Monotonicity, convexity and inflection points of differentiable functions, Graphing functions
XIV week exercises	Monotonicity, convexity and inflection points of differentiable functions, Graphing functions
XV week lectures	Makeup exam
XV week exercises	Makeup exam

Student workload
Per week	Per semester
7 credits x 40/30=9 hours and 20 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 3 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 9 hour(s) i 20 minuts x 16 =149 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 9 hour(s) i 20 minuts x 2 =18 hour(s) i 40 minuts Total workload for the subject: 7 x 30=210 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 42 hour(s) i 0 minuts Workload structure: 149 hour(s) i 20 minuts (cources), 18 hour(s) i 40 minuts (preparation), 42 hour(s) i 0 minuts (additional work)
Student obligations	Students are encouraged to attend classes regularly, although this is not mandatory. However, it is doubtful that one will do well in the course if you miss too many lectures.
Consultations	As agreed with the professor or teaching assistant.
Literature	1. Z. Kaldeburg, V. Mićić, S. Ognjanović, Analiza sa algebrom III, ”Krug” Beograd, 2000. 2. James Stewart, Early Transcendentals 6, ISBN-13: 978-0-495-01166-8, 2008.
Examination methods	Тhe forms of testing and grading 1. Midterm exam (up to 45 points) and Final exam (up to 45 points). 2. The points awarded for special commitment (up to 10 points). Grading scale: F (below 50 points), E (50-59 points), D (60-69), C (70-79), B (80-8
Special remarks
Comment	If opportunity to take a makeup test, or correctional final exam is used, then the results achieved on them will be treated as definitive.

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / COMPUTERS AND PROGRAMMING

Course:

COMPUTERS AND PROGRAMMING/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
495	Obavezan	1	3	2+1+0

Programs	PHYSICS
Prerequisites
Aims	The aim of this introductory course in programming is to acquaint students with the basic programming skills necessary to analyse and solve simple physics problems and process and present experimental results obtained in lab. Students will be introduced to the basic concepts of programming in the C programming language and elementary numerical algorithms used to solve the general equation of Newtons dynamics.
Learning outcomes	After passing this exam, students will be able to: 1. process the experimental results and prepare report for the laboratory exercise with tables, results and graphs in Latex, Power point / LibreOffic and Gnuplot; 2. design an algorithm and solution of a simple task and implement it in a specific programming language; 3. apply numerical methods to solve the general equation of motion; 4. analyse and test the program and find potential errors; 5. learn independently and search for information (especially on the Internet) needed to solve tasks.
Lecturer / Teaching assistant	Nataša Raičević
Methodology	Lectures, tutorials, consultations, seminar paper, test, midterm exam, final exam.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Introductory remarks. Basic commands in the LINUX operating system.
I week exercises	Mastering basic LINUX commands
II week lectures	Editors. Basic word processing commands in LaTex.
II week exercises	Introduction to the Emacs editor. Structuring a document in LaTex.
III week lectures	Lab report in LaTex.
III week exercises	Formulas, tables, images, graphics in LaTex.
IV week lectures	Lab report in Microsoft Power Pont/LibreOffice.
IV week exercises	Formulas, tables, images, graphics in Microsoft Power Pont/LibreOffice.
V week lectures	Program structure in C. Variables and constants. Printf and Scanf functions.
V week exercises	Tasks related to lectures from the current week
VI week lectures	Arithmetics and operators. Conditional stetements.
VI week exercises	Tasks related to lectures from the current week
VII week lectures	Loops.
VII week exercises	Tasks related to lectures from the current week
VIII week lectures	Jump statements. Arrays.
VIII week exercises	Tasks related to lectures from the current week
IX week lectures	Functions.
IX week exercises	Tasks related to lectures from the current week
X week lectures	Structures. Files.
X week exercises	Tasks related to lectures from the current week
XI week lectures	Midterm exam.
XI week exercises
XII week lectures	Gnuplot. Presentation of experimental results obtained in Lab I using Gnuplot.
XII week exercises	Tasks related to lectures from the current week.
XIII week lectures	Eulers method for solving the general equation of motion.
XIII week exercises	Eulers method for solving the general equation of motion - writing programs
XIV week lectures	More accurate numerical methods for solving the general equation of motion.
XIV week exercises	More accurate numerical methods for solving the general equation of motion - writing programs.
XV week lectures	Seminar paper defense.
XV week exercises	Seminar paper defense.

Student workload
Per week	Per semester
3 credits x 40/30=4 hours and 0 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 1 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts Total workload for the subject: 3 x 30=90 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 18 hour(s) i 0 minuts Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to attend classes regularly, as well as doing test, midterm exam and final exam.
Consultations	Office 112 Monday: 14:00 Thursday: 14:00 Consultations can also be scheduled by email (natasar@ucg.ac.me)
Literature	1. Oxford University Computing IT tutorial: PHYSICS C PROGRAMMING COURSE http://www-teaching.physics.ox.ac.uk/computing/handbook_C.pdf 2. Laslo Kraus, Rešeni zadaci iz programskog jezika C, Akademska misao, 2014. 3. Dragomir Krpić, Uvod u numeričku fiziku i C/C++ WINDOWS programiranje, ICNT, 2008, univerzitetski udžbenik.
Examination methods	Students can receive a maximum of 15 points for a successfully completed seminar paper, a maximum of 35 points in the midterm exam (preceded by a test that carries 7 points) and a maximum of 50 points in the final exam. In order to pass the exam, students must earn at least 50 points.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ANALYSIS II

Course:

ANALYSIS II/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
496	Obavezan	2	7	3+3+0

Programs	PHYSICS
Prerequisites
Aims	The aim of the course is mastering the basics of mathematical analysis: the concept of definite and indefinite integral, multiple and functional lines.
Learning outcomes	After passing this exam, the student should be able to 1. Defines the notion of definite and indefinite integral and their connection through the Newton-Leibniz formula. 2. Find definite and indefinite integrals using techniques like substitution rule, trigonometric integration, integration by parts, integration of rational functions ... 3. Compute the area bounded by multiple curves and the volume of a solids that are obtained by revolving of that plane region about a horizontal or vertical line. 4. Uses various tests in order to determine the convergence of the series, compute Taylor's representation of certain functions. 5. Defines the basic notions and results related to the Fourier series.
Lecturer / Teaching assistant	Vladimir Božović and Dušica Slović
Methodology	Lectures, exercises, independent work, and consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	The notion of indefinite and definite integrals, Areas and distances
I week exercises	The notion of indefinite and definite integrals, Areas and distances
II week lectures	The Fundamental Theorem of Calculus, Table of elementary integrals and substitution rule
II week exercises	The Fundamental Theorem of Calculus, Table of elementary integrals and substitution rule
III week lectures	Area between two curves, Volume
III week exercises	Area between curves, Volume
IV week lectures	Integration by Parts, Trigonometric integrals, Trigonometric substitutions
IV week exercises	Integration by Parts, Trigonometric integrals, Trigonometric substitutions
V week lectures	Integration of Rational Functions by Partial Fractions, Strategy for Integrations, Approximate integrations
V week exercises	Integration of Rational Functions by Partial Fractions, Strategy for Integrations, Approximate integrations
VI week lectures	Improper integrals, Arc length and Center of mass
VI week exercises	Improper integrals, Arc length and Center of mass
VII week lectures	Series, Integral test and estimates of sums
VII week exercises	Series, Integral test and estimates of sums
VIII week lectures	Midterm exam
VIII week exercises	Midterm exam
IX week lectures	The comparison test, Alternating series
IX week exercises	The comparison test, Alternating series
X week lectures	Ratio and Root test, Strategy for testing series
X week exercises	Ratio and Root test, Strategy for testing series
XI week lectures	Power series, Representations of functions as power series
XI week exercises	Power series, Representations of functions as power series
XII week lectures	Taylor and Maclaurin series
XII week exercises	Taylor and Maclaurin series
XIII week lectures	Applications of Taylor polynomials
XIII week exercises	Applications of Taylor polynomials
XIV week lectures	Fourier series and Fourier transformation
XIV week exercises	Fourier series and Fourier transformation
XV week lectures	Makeup exam
XV week exercises	Makeup exam

Student workload
Per week	Per semester
7 credits x 40/30=9 hours and 20 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 3 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 9 hour(s) i 20 minuts x 16 =149 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 9 hour(s) i 20 minuts x 2 =18 hour(s) i 40 minuts Total workload for the subject: 7 x 30=210 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 42 hour(s) i 0 minuts Workload structure: 149 hour(s) i 20 minuts (cources), 18 hour(s) i 40 minuts (preparation), 42 hour(s) i 0 minuts (additional work)
Student obligations	Students are encouraged to attend classes regularly, although this is not mandatory. However, it is doubtful that one will do well in the course if you miss too many lectures.
Consultations	As agreed with the professor or teaching assistant.
Literature	James Stewart, Early Transcendentals 6, ISBN-13: 978-0-495-01166-8, 2008.
Examination methods	Тhe forms of testing and grading 1. Midterm exam (up to 45 points) and Final exam (up to 45 points). 2. The points awarded for special commitment (up to 10 points). Grading scale: F (below 50 points), E (50-59 points), D (60-69), C (70-79), B (80-8
Special remarks
Comment	If opportunity to take a makeup test, or correctional final exam is used, then the results achieved on them will be treated as definitive.

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / DIFFERENTIAL EQUATIONS

Course:

DIFFERENTIAL EQUATIONS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
497	Obavezan	3	4	2+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 1 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ANALYSIS III

Course:

ANALYSIS III/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
501	Obavezan	3	6	3+2+0

Programs	PHYSICS
Prerequisites	Analysis 1 and Analysis 2
Aims	In the frame of the course, students are acquainted with notions of metrics, continuity, differentiability, theory of extremal values and integrability of multidimensional real functions. Notions of line integrals and and integral over manifolds as well as their connection (Gauss-Ostrogradskii and Stokes formula)
Learning outcomes	After passing this exam, will be able to: It describes the topology of Euclidean space Differentiating features more variables Located conditional and local ekstremum function more variables Calculates multiple integrals Solves problems surface, volume and length wrong.
Lecturer / Teaching assistant	Darko Mitrović Đorđije Vujadinović
Methodology	Lectures, practical problems, homework, written and oral tests. Consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Rn-space; metrics and topological properties.
I week exercises
II week lectures	Sequences in Rn. Convergence in Rn. Compactness.
II week exercises
III week lectures	Real functions of several variables (multidimensional functions in the sequel). Basic properties.
III week exercises
IV week lectures	Limit values of real multidimensional functions.
IV week exercises
V week lectures	Continuity of multidimensional functions and properties of the continuous functions.
V week exercises
VI week lectures	Partial derivatives. Differentiability. Directional derivatives. Gradient.
VI week exercises
VII week lectures	Partial derivatives of higher orders. I colloquium
VII week exercises
VIII week lectures	Taylor formula. Local extremum. Correction of I colloquium
VIII week exercises
IX week lectures	Conditional extremum.
IX week exercises
X week lectures	Definition of multidimensional integral. Integrability criterion and basic properties
X week exercises
XI week lectures	Computation of multidimensional integrals. Change of variables.
XI week exercises
XII week lectures	Line integral of first and second kind. Greens theorem.
XII week exercises
XIII week lectures	Space integral of first and second kind.
XIII week exercises
XIV week lectures	II coloquium
XIV week exercises
XV week lectures	Correction of II colloquium
XV week exercises

Student workload	8hours/week
Per week	Per semester
6 credits x 40/30=8 hours and 0 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 3 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts Total workload for the subject: 6 x 30=180 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 36 hour(s) i 0 minuts Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations	Lectures, practical problems, homework, written and oral tests. Consultations.
Consultations	2 hours/week
Literature	D. Adnađević, Z. Kadelburg: Matematička analiza II, Beograd; M. Ušćumlić, P. Miličić: Zbirka zadataka iz Više matematike II, Beograd; M. Jaćimović: Skripta.
Examination methods	2 colloquiums 30 points each (60 points). 2 homeworks 4 point each (8 points). Attending classes: 2 points. Final exam - 30 points. Success level is 50 points.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / PROBABILITY THEORY AND STATISTICS

Course:

PROBABILITY THEORY AND STATISTICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
504	Obavezan	4	4	2+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 1 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / LINEAR ALGEBRA AND ANALITICAL GEOMETRY

Course:

LINEAR ALGEBRA AND ANALITICAL GEOMETRY/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
524	Obavezan	1	5	2+2+0

Programs	PHYSICS
Prerequisites	None
Aims	This course is aimed to introduce students with basic notions of linear algebra and analytical geometry and its applications in mathematical and technical science.
Learning outcomes	On successful completion of the course, students will be able to: - define basic mathematical concepts (set, relation, function, mapping) - define basic algebraic structures (groupoids, semigroups, monoide, groups, rings, fields) - define concepts of vector spaces, subspaces, basis and dimension, linear dependence (independence) of vectors, determinant, matrix and rank, linear mapping of vector spaces, conjugated and self-conjugated operator, orthogonal and normal operator - calculate the value of a determinant and master matrix calculations, especially calculating the inverse matrix - solve a system of linear equations (using the Cramer rule, Cronecker-Capelli theorem, Gauss algorithm, with proof and discussion ) - define matrix similarity, find eigenvalues and eigenvectors of a matrix and write the Jordan canonic form of a matrix - describe the line and plane, write corresponding equations in scalar form and solve suitable problems - describe second order surfaces (cylindric, conic, spheric and rotational, ellipsoids, hyperboloids and paraboloids ), write their equations and solve suitable problems
Lecturer / Teaching assistant	Prof. dr Biljana Zeković
Methodology	Lectures, exercises, consultations, homework assignments

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Introduction. Basic mathematical concepts (sets)
I week exercises	Introduction. Basic mathematical concepts (sets)
II week lectures	Relations. Functions
II week exercises	Relations. Functions
III week lectures	Basic algebraic structures
III week exercises	Basic algebraic structures
IV week lectures	Vector spaces
IV week exercises	Vector spaces
V week lectures	Linear maps of vector spaces (matrices) (First homework assignment)
V week exercises	Linear maps of vector spaces (matrices) (First homework assignment)
VI week lectures	Polilinear mappings (determinants)
VI week exercises	Polilinear mappings (determinants)
VII week lectures	Laplace expansion of a determinant.
VII week exercises	Laplace expansion of a determinant.
VIII week lectures	Inverse matrix
VIII week exercises	Inverse matrix
IX week lectures	Systems of linear equations. I written exam.
IX week exercises	Systems of linear equations. I written exam.
X week lectures	Factorization of a polynomial. Eigenvectors and eigenvalues
X week exercises	Factorization of a polynomial. Eigenvectors and eigenvalues
XI week lectures	Matrix similarity. Jordan canonical form (Second homework assignment)
XI week exercises	Matrix similarity. Jordan canonical form (Second homework assignment)
XII week lectures	Operators (conjugate, ortogonal, normaln). Bilinear and quadratic form
XII week exercises	Operators (conjugate, ortogonal, normaln). Bilinear and quadratic form
XIII week lectures	Euclidean linear spaces (scalar, vector and mixed product and basic properties). II written exam
XIII week exercises	Euclidean linear spaces (scalar, vector and mixed product and basic properties). II written exam
XIV week lectures	Line, plane and relation (Third homework assignment.).
XIV week exercises	Line, plane and relation (Third homework assignment.).
XV week lectures	Surfaces of second order (cylinder ,conic, sphere and rotary) and classification
XV week exercises	Surfaces of second order (cylinder ,conic, sphere and rotary) and classification

Student workload	2 hours of lectures, 2 hours of exercises, 2 hours 40 minutes of individual work
Per week	Per semester
5 credits x 40/30=6 hours and 40 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts Total workload for the subject: 5 x 30=150 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 30 hour(s) i 0 minuts Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations	Attendance, doing homework assignments, taking two written and the final exam
Consultations	1 hour weekly
Literature	Linearna algebra i analitička geometrija, V.Dašić; Zbirka rešenih zadataka iz Linearne algebre i analitičke geometrije, M. Kosmajac
Examination methods	I written exam - 21 point; II written exam - 21 point; Attendance - 2 points; Doing homework assignments - 6 points. In total - 50 points. Final exam - 50 points. Everything is in written form, with oral examination in case of any unclarity or doubt
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ELECTROMAGNETISM

Course:

ELECTROMAGNETISM/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
529	Obavezan	3	8	4+4+0

Programs	PHYSICS
Prerequisites	None.
Aims	The primary goal of this course is to understand the physical properties of basic electric, magnetic and electromagnetic phenomena and show how these are described by advanced vector analysis. A good understanding of the physical phenomena and mathematical apparatus used in the theory of electromagnetism provide the knowledge and skills which required for further education in physics.
Learning outcomes	On completion of this course the student shall be able to: 1. define the basic laws of electrostatics; 2. define the basic laws of magnetostatics; 3. define the basic laws of time-varying electric and magnetic fields; 4. analyse DC and AC circuits; 5. interpret physically the basic concepts and theorems from vector analysis necessary for the theory.
Lecturer / Teaching assistant	Prof. dr Nataša Raičević, dr Krsto Ivanović
Methodology	Lectures, tutorials, 2 midterm exams, final exam.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Introduction. Electrostatic interaction. Coulomb’s law
I week exercises	Elements of vector analysis: vector algebra, differential calculus, integral calculus, spherical polar and cylindrical coordinates.
II week lectures	The electric field in vacuum. The electric potential. Potential energy. Voltage. Gauss’ law.
II week exercises	Tasks related to lectures from the previous and/or current week.
III week lectures	Poisson’s equation. Electric dipole. Dipole in an electric field. Molecule electrostatic potential.
III week exercises	Tasks related to lectures from the previous and/or current week.
IV week lectures	Polarization. Distribution of bound charge. The displacement field. Electrostatic boundary conditions.
IV week exercises	Tasks related to lectures from the previous and/or current week.
V week lectures	Conductors in electrostatic equilibrium. Electrostatic induction. Capacitance and capacitors. Metod of mirror images.
V week exercises	Tasks related to lectures from the previous and/or current week.
VI week lectures	Electric field energy. Electrostatic pressure on a conducting surface. Electrostatic pressure on a dielectric surface.
VI week exercises	Tasks related to lectures from the previous and/or current week.
VII week lectures	Electric current. Electric current density. Steady current. Electromotive force. Ohm’s law. Kirchhoff’s laws. Joule-Lenz law.
VII week exercises	Tasks related to lectures from the previous and/or current week.
VIII week lectures	Interaction betweem mooving charges. Lorentz force. Magnetic field in vacuum. The Biot-Savart law. The divergence and curl of vector B. Ampere’s law.
VIII week exercises	Tasks related to lectures from the previous and/or current week.
IX week lectures	The vector potential. Magnetic field due to a circular current loop. Magnetic dipole moment. Current loop in a magnetic field. Multipole expansion of the vector potential.
IX week exercises	Tasks related to lectures from the previous and/or current week.
X week lectures	I midterm exam. The magnetic field of a solenoid and toroidal coil. The magnetic moment of a molecule. Magnetization. Bound currents. Magnetization surface current.
X week exercises	Tasks related to lectures from the previous and/or current week.
XI week lectures	Magnetic field strength vector. Magnetostatic boundary conditions. Diamagnets, paramagnets and ferromagnets.
XI week exercises	Tasks related to lectures from the previous and/or current week.
XII week lectures	Electromagnetic induction. Faraday’s law. Self-inductance. Mutual inductance. Magnetic field energy.
XII week exercises	Tasks related to lectures from the previous and/or current week.
XIII week lectures	Quasi-steady current. Free oscillations in LC circuit. Two coupled LC circuits.
XIII week exercises	Tasks related to lectures from the previous and/or current week.
XIV week lectures	Damped oscilations in RLC circuit. Alternating current. Power in alternating-current circuits. Rezonance curves.
XIV week exercises	Tasks related to lectures from the previous and/or current week.
XV week lectures	II midterm exam. Transformers. Three-phase current. Eddy current. The Mawxell equations.
XV week exercises	Tasks related to lectures from the previous and/or current week.

Student workload	Weekly: 10 ECTS x 40/30=13 hours and 20 min. ~ 13.5 hours. 4 hours of lectures,4 hours exercises,5.5 hours additional work including consultations. In semester: Teaching and final exam: (8 hours) x 16 = 128 hours The necessary preparations before the start of the semester (administration, enrollement, certification) 2 x 13.5 hour = 27 hour. Total hours for the course 10x30 = 300 hours.
Per week	Per semester
8 credits x 40/30=10 hours and 40 minuts 4 sat(a) theoretical classes 0 sat(a) practical classes 4 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts Total workload for the subject: 8 x 30=240 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 48 hour(s) i 0 minuts Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to attend classes regularly, as well as doing both midterm exams and final exam.
Consultations	Office 112 Monday: 14:00 Thursday: 14:00 Consultations can also be scheduled by email (natasar@ucg.ac.me)
Literature	1. D. Burzan, Elektromagnetizam – skripta, Podgorica. 2. I. V. Savelьev, Kurs obщeй fiziki, tom 2 – эlektričestvo i magnetizam, “Nauka”, Moskva 1982. 3. I. Irodov, Zbirka zadataka iz opšte fizike, Zavod za udžbenike i nastavna sredstva, P
Examination methods	Each homework assignment is worth 2 points (all together 10 points), each midterm exam is worth 25 points (all together 50 points) and the final exam is worth 40 points. A student needs 51 points in order to pass the exam.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / HISTORY AND PHILOSOPHY OF PHYSICS

Course:

HISTORY AND PHILOSOPHY OF PHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
532	Obavezan	5	4	2+0+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 0 excercises 3 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / NUMERICAL METHODS

Course:

NUMERICAL METHODS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
533	Obavezan	4	4	2+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 1 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / OPTICS

Course:

OPTICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
534	Obavezan	4	4	3+2+0

Programs	PHYSICS
Prerequisites	entered the second year of study
Aims	The aim of the course is that students understand the physical background of the basic phenomena of light and its electromagnetic nature. The polarization, diffraction, interference and their application in modern optical systems are the main focus in this course.
Learning outcomes	After passing this exam the student will be able to: 1. Understand the concept of geometric and wave optics; 2. Understand and explain the basic optical phenomena such as reflection, refraction, interference, diffraction and polarization; 3. Solve basic problems in classical optics, by analytical and graphical methods; 4. Apply basic knowledge of optics in the analysis of modern optical instruments; 5. Understand and explain the electromagnetic nature of light.
Lecturer / Teaching assistant	Slavoljub Mijovic and Stevan Đurđević
Methodology	Lectures, calculation exercises, consultations;

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Overview of the historical development of the ideas of light; Four basic laws of geometrical optics;
I week exercises	Solving basic tasks in geometrical optics;
II week lectures	Geometric optics: Fermats principle; elements of optical systems, optical prism;
II week exercises	Analytical and graphical solution of tasks of geometrical optics;
III week lectures	Luminous flux, photometry, propagation of light;
III week exercises	Solving practical tasks of photometry;
IV week lectures	Waves; Wave equation; Maxwells equations in integral and differential form; The mathematical formalism;
IV week exercises	Solving general problems of waves;
V week lectures	Electromagnetic nature of light; Poyintigs vector;
V week exercises	Solving the problem of power transmission by electro-magnetic waves
VI week lectures	First test. (maximum 30 points)
VI week exercises	Repetition
VII week lectures	Interference of light: general considerations, the temporal coherence of light; The spatial coherence of light, interference in plane-parallel plate, interference on a transparent wedge;
VII week exercises	Solving general problems in interferometry;
VIII week lectures	Youngs experiment, Fresnels mirror, Fresnels biprizma, Loyds mirror; Newtons rings, Michelsons interferometer, Fabry-Perots interferometer;
VIII week exercises	Solving problems of classical interferometry;
IX week lectures	Diffraction; Huygens-Fresnels principle; Rayleighs criterion; Method of Fresnels zone; The graphical methods;
IX week exercises	Solving general problems of diffraction by analytical and graphical methods;
X week lectures	Fraunhofer diffraction;
X week exercises	Solving the problems of diffraction by analytical and graphical methods;
XI week lectures	The optical grating; Dispersion and resolving power;
XI week exercises	Solving practical problems of spectroscopy;
XII week lectures	The second test (maximum 30 points);
XII week exercises	Repetition
XIII week lectures	General problems of polarization of light; Malus law;
XIII week exercises	Solving examples of polarization;
XIV week lectures	Line, circular and elliptical polarization;
XIV week exercises	Solving the problems of polarization;
XV week lectures	Birefringence in crystals; Plates of quarter and half wave;
XV week exercises	Using EMANIM program for visualizations of various cases of polarization;

Student workload	4 hours of lectures; 2 hours of exercises;
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 0 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to attend lectures and exercises (maximum three excused absences);
Consultations	Wednesdays from 10-12 hours
Literature	E. Hecht Optics; Optics Matveev A. N. (in english). Hardcover. 448 pp .; Physics: A General Course. V.II. Savelyev IV (in russian). Hardcover. 512 pp; Physics II (Electromagnetism and Optics) Ivanovic D. Vasić; I. Irodov, Problems in General Physics, Inst
Examination methods	homework - 5 points; seminar -5 points; First test - 30 points; Second test - 30 points; Final exam - 30 points
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / MATHEMATICAL METHODS IN PHYSICS

Course:

MATHEMATICAL METHODS IN PHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
535	Obavezan	5	8	3+2+0

Programs	PHYSICS
Prerequisites	Math I, Math II and Elektromangnetizam.
Aims	In the frame of the course, students are acquainted with different mathematical tools that are used in physics.
Learning outcomes	After passing this exam, a student: Applies variations in analytical mechanics Connects the theory of probability to the concept of entropy and second law of thermodynamics Applies special functions (orthogonal polynomials) in atomic and quantum physics Uses tensor and tensor algebra understands elements Applies the theory group in solid-state physics and quantum chemistry. Applies theory of representation groups and infinite groups in quantum mechanics, the physics of elementary particles and the theory of relativity
Lecturer / Teaching assistant	Gordana Jovanović
Methodology	Attending lectures, exercises, consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Vector spaces. Linear (in)dependence. Base and dimension.
I week exercises	Vector spaces. Linear (in)dependence. Base and dimension.
II week lectures	Isomorphism. Scalar product. Orthonormality.
II week exercises	Isomorphism. Scalar product. Orthonormality.
III week lectures	Bessel and Schwarz inequality.Gram-Schmidt orthonormalization procedure.
III week exercises	Bessel and Schwarz inequality.Gram-Schmidt orthonormalization procedure.
IV week lectures	Subspaces. Operations with subspaces. Projection theorem.
IV week exercises	Subspaces. Operations with subspaces. Projection theorem.
V week lectures	Linear operators. Definition and examples. Vector space. Algebra.
V week exercises	Linear operators. Definition and examples. Vector space. Algebra.
VI week lectures	Geometry of operator action. Defect and operator rank. (Non)singularity and invertibility.
VI week exercises	Geometry of operator action. Defect and operator rank. (Non)singularity and invertibility.
VII week lectures	Rank of matrix. Systems of linear equations.
VII week exercises	Rank of matrix. Systems of linear equations.
VIII week lectures	Representation and change of base. Invariant subspaces.
VIII week exercises	Representation and change of base. Invariant subspaces.
IX week lectures	Colloquium.
IX week exercises	Colloquium.
X week lectures	Operators in spaces with scalar product. Linear functionals. Adjunct operator.
X week exercises	Operators in spaces with scalar product. Linear functionals. Adjunct operator.
XI week lectures	Basic features and types of operators. Normal operators. Hermitian operators.
XI week exercises	Basic features and types of operators. Normal operators. Hermitian operators.
XII week lectures	Projectors. Unitary and orthogonal operators.
XII week exercises	Projectors. Unitary and orthogonal operators.
XIII week lectures	Spectral theory. An inherent problem.
XIII week exercises	Spectral theory. An inherent problem.
XIV week lectures	A peculiar problem in complex space.
XIV week exercises	A peculiar problem in complex space.
XV week lectures	An inherent problem in real space.
XV week exercises	An inherent problem in real space.

Student workload	weekly 6 credits x 40/30 = 8 hours Structure: 3 hours of lectures 2 hours of computational exercises 3 hours and 45 minutes of independent work, including consultation During the semester Classes and final exam: 8 hours x 16 = 128 hours Necessary preparations before the beginning of the semester (administration, registration, certification) 2 x 8 hours = 16 hours
Per week	Per semester
8 credits x 40/30=10 hours and 40 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 5 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts Total workload for the subject: 8 x 30=240 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 48 hour(s) i 0 minuts Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations	Attending lectures, exercises, consultations, colloquium and final exam.
Consultations	agreement with students
Literature	Literature: Ivanka Milošević, Vektorski prostori i elementi vektorske analize , Univerzitet u Beogradu, 1997. Tatjana Vuković, Saša Dmitrović, Osnovi matematičke fizike, Univerzitet u Beogradu, ISBN 978-86-84539-15-3 K.F. Riley, M.P. Hobson, Essential Mathematical Methods for the Physical Sciences, Cambridge University Press, 2011.
Examination methods	• Colloquium 40 points • Final exam 60 points. • A passing grade is obtained if at least 51 points are accumulated cumulatively.
Special remarks	none
Comment	Classes are carried out for a group of about 10 students.

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / STATISTICAL PHYSICS

Course:

STATISTICAL PHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
538	Obavezan	5	10	4+3+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
10 credits x 40/30=13 hours and 20 minuts 4 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 6 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 13 hour(s) i 20 minuts x 16 =213 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 13 hour(s) i 20 minuts x 2 =26 hour(s) i 40 minuts Total workload for the subject: 10 x 30=300 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 60 hour(s) i 0 minuts Workload structure: 213 hour(s) i 20 minuts (cources), 26 hour(s) i 40 minuts (preparation), 60 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / SOLID STATE PHYSICS

Course:

SOLID STATE PHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
543	Obavezan	6	5	3+1+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
5 credits x 40/30=6 hours and 40 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts Total workload for the subject: 5 x 30=150 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 30 hour(s) i 0 minuts Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / QUANTUM MECHANICS

Course:

QUANTUM MECHANICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
999	Obavezan	6	5	3+1+0

Programs	PHYSICS
Prerequisites	Classical mechanics
Aims	Introduction to the basic laws of physics that apply at the level of atoms and their nuclei
Learning outcomes	Upon completion of this course the student will be able to: 1. reproduce basic quantum mechanical results for spin 1/2 2. use the technique of time-independent theory of perturbacine 3. understand radiation emission and absorption 4. explain the alternating interaction in identical particles 5. explain the schedule in the periodic table of elements
Lecturer / Teaching assistant	Prof. dr Predrag Miranović, lecturer; mr Stevan Đurđević, assistant
Methodology	lectures, exercises, consultations

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Spin
I week exercises
II week lectures	Addition of angular momenta
II week exercises
III week lectures	Identical particles
III week exercises
IV week lectures	Two-particle system
IV week exercises
V week lectures	Atoms and crystals
V week exercises
VI week lectures	Stationary theory of perturbation
VI week exercises
VII week lectures	Perturbation of degenerate energy level
VII week exercises
VIII week lectures	Hydrogen fine structure. Zeeman effect
VIII week exercises
IX week lectures	Variational principle. Ground state of helium
IX week exercises
X week lectures	Hydrogen molecule ion
X week exercises
XI week lectures	Time dependent theory of perturbation, Two-level system
XI week exercises
XII week lectures	Radiation emission and absorption
XII week exercises
XIII week lectures	Spontaneous emission
XIII week exercises
XIV week lectures	Scattering theory. Partial wave analysis
XIV week exercises
XV week lectures	Born approximation
XV week exercises

Student workload
Per week	Per semester
5 credits x 40/30=6 hours and 40 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts Total workload for the subject: 5 x 30=150 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 30 hour(s) i 0 minuts Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to attend classes regularly.
Consultations	Every week on request
Literature	1. Introduction to quantum mechanics, D. J. Griffiths, Prentice Hall, New Jersey 2005
Examination methods	Tests (40 points), homework (10 points), final exam (50 points).
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ENGLISH LANGUAGE I

Course:

ENGLISH LANGUAGE I/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1093	Obavezan	1	3	2+1+0

Programs	PHYSICS
Prerequisites	There are no pre-requisites for the course. However, the students should command upper-intermediate English in order to be able to follow the classes.
Aims	Mastering basic English for physics.
Learning outcomes	After passing the exam the student will be able to: - differentiate, understand and use the basic physics terminology in English at the B2.3 level; understand the messages of popular and expert physics texts, as well as general texts, written in English, at the B2.3 level; - independently communicate in an oral and written form in English, at the B2.3 level; - explain his/her ideas by integrating the basic grammar structures and speaking skills, at the B2.3 level.
Lecturer / Teaching assistant	Milica Vuković Stamatović
Methodology	A short introduction to the topics covered, with the focus on the participation of students in various types of exercises - conversation and writing, pairwork, groupwork, presentations, discussions etc.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Introduction to the course
I week exercises
II week lectures	Numbers and dimensions. Unit 1: Why is the ocean blue?
II week exercises
III week lectures	Describing objects. Unit 1: Light
III week exercises
IV week lectures	Describing shape, size, use. Revision of Unit 1
IV week exercises
V week lectures	Describing angles and lines. Unit 2: Technology: inventing a telephone
V week exercises
VI week lectures	Reading basic formulae. Unit 2: A mirror or a mirage?
VI week exercises
VII week lectures	Reading more complex formulae. Revision of Unit 2. Preparation for the mid-term test.
VII week exercises
VIII week lectures	Mid-term test
VIII week exercises
IX week lectures	Describing position. Unit 3: The power of wind
IX week exercises
X week lectures	Describing movement and action. Unit 3: How does a roller coaster work?
X week exercises
XI week lectures	Describing direction. Revision of grammar
XI week exercises
XII week lectures	Mid-term test (2nd term)
XII week exercises
XIII week lectures	Describing qualities of materials. Presentations
XIII week exercises
XIV week lectures	Describing colours and appearance. Describing a simple process and experiment.
XIV week exercises
XV week lectures	Prepration for the final exam.
XV week exercises

Student workload	2 hours 40 minutes
Per week	Per semester
3 credits x 40/30=4 hours and 0 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 1 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts Total workload for the subject: 3 x 30=90 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 18 hour(s) i 0 minuts Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations	Regular attendance, presenting in class, taking the mid-term and the final exam.
Consultations
Literature	Basic English for Science, Donovan, P. Oxford University Press: 1978. Communicative English for Physicists, Antonova et al., 2012
Examination methods	Mid-term test: 40 points Presentation: 5 points Attendance: 5 points Final exam: 50 points
Special remarks	Classes are in English.
Comment	-

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ENGLISH LANGUAGE II

Course:

ENGLISH LANGUAGE II/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1094	Obavezan	2	3	2+1+0

Programs	PHYSICS
Prerequisites	There are no pre-requisites for the course. However, the students should command upper-intermediate English in order to be able to follow the classes.
Aims	To master the basic grammar structures and use the English language in everyday situations. To understand professional texts and speak on topics from the field of physics.
Learning outcomes	After passing the exam, the students will be able to: - Understand the basic messages of the more complex popular-professional English texts in the field of physics, - Command the basic English vocabulary in the field of physics from the areas covered in classes (resonance, composite materials, minerals, theories about the origin of the universe, gravity, quantum physics), - Present in English on the chosen topic from the area of physics, - Write a summary and a review of a popular-professional text or audio recording in English.
Lecturer / Teaching assistant	Milica Vuković
Methodology	A short introduction to the topics covered, with the focus on the participation of students in various types of exercises - conversation and writing, pairwork, groupwork, presentations, discussions etc.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Introduction to the course
I week exercises
II week lectures	Unit 4: The sound of music
II week exercises
III week lectures	Unit 5: The 787 dreamliner and composite materials
III week exercises
IV week lectures	Unit 6: Why do fish swim?
IV week exercises
V week lectures	Unit 7: Minerals and gems
V week exercises
VI week lectures	Unit 8: Jobs for physicists. Preparation for the mid-term test.
VI week exercises
VII week lectures	Mid-term test
VII week exercises
VIII week lectures	Atomic theory of matter; Temperature and thermometers
VIII week exercises
IX week lectures	Vibrations and waves; 4-dimensional space-time
IX week exercises
X week lectures	Big bang theory; How does a satellite stay in orbit?
X week exercises
XI week lectures	Why do things float? Time travel
XI week exercises
XII week lectures	Teleportation; Quantum mechanics of atom
XII week exercises
XIII week lectures	The beginning of time
XIII week exercises
XIV week lectures	Mid-term test (2nd term)
XIV week exercises
XV week lectures	Preparation for the final exam
XV week exercises

Student workload	2 hours 40 minuts
Per week	Per semester
3 credits x 40/30=4 hours and 0 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 1 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts Total workload for the subject: 3 x 30=90 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 18 hour(s) i 0 minuts Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations	Regular attendance, presenting in class
Consultations
Literature	English for Physicists, Antonova et al., 2012; A selection of texts analysed in classes
Examination methods	Mid-term test: 35 points Presentation: 15 points Attendance: 5 points Final exam: 45 points
Special remarks	Classes are in English.
Comment	-

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / MATHEMATICS I

Course:

MATHEMATICS I/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1310	Obavezan	1	8	3+3+0

Programs	PHYSICS
Prerequisites
Aims	The aim of the course is mastering the basics of mathematical analysis: the notion of convergence, practical methods for calculation of limit values, elements of differential calculus and its applications in the graphics drawing functions.
Learning outcomes	After passing this exam, the student should be able to 1. Defines the notion of convergent sequence and successfully use various techniques for finding the limit values and prove the convergence of a sequence. 2. Find limit values of functions and determines intervals of their continuity. 3. Make a graph of basic and complex functions. 4. Determines derivatives of basic and complex functions. 5. Use derivatives and The Mean Value Theorem to solve some practical problems in physics, as well as the maximum and minimum problems.
Lecturer / Teaching assistant	Vladimir Božović and Dušica Slović
Methodology	Lectures, exercises, independent work, and consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Review - notion of a sequence, Arithmetic and Geometric sequence.
I week exercises	Review - notion of a sequence, Arithmetic and Geometric sequence.
II week lectures	The notion of convergence, Convergent sequences - definition and examples
II week exercises	The notion of convergence, Convergent sequences - definition and examples
III week lectures	Properties of convergent sequences, Monotone sequences, Number e as a limit of the seqeunce
III week exercises	Properties of convergent sequences, Monotone sequences, Number e as a limit of the seqeunce
IV week lectures	Some interesting application of sequences - Examples in Physics
IV week exercises	Some interesting application of sequences - Examples in Physics
V week lectures	The nootion of series - series as a sequence, Properties of series
V week exercises	The nootion of series - series as a sequence, Properties of series
VI week lectures	The limit of a function, Calculating limits using the limit laws
VI week exercises	The limit of a function, Calculating limits using the limit laws
VII week lectures	The precise definition of a limit, Continuity
VII week exercises	The precise definition of a limit, Continuity
VIII week lectures	Midterm exam
VIII week exercises	Midterm exam
IX week lectures	Derivatives, The derivative as a function, Derivatives of elementary functions
IX week exercises	Derivatives, The derivative as a function, Derivatives of elementary functions
X week lectures	The Chain Rule, Derivatives of functions in implicit and parametric form
X week exercises	The Chain Rule, Derivatives of functions in implicit and parametric form
XI week lectures	Applications of differentiation, Maximum and minimum values, The Mean Value Theorem
XI week exercises	Applications of differentiation, Maximum and minimum values, The Mean Value Theorem
XII week lectures	How derivatives affect the shape of a graph, Indeterminate forms and L’Hospital’s rule, Review
XII week exercises	How derivatives affect the shape of a graph, Indeterminate forms and L’Hospital’s rule, Review
XIII week lectures	Taylor and Maclaurin Series
XIII week exercises	Taylor and Maclaurin Series
XIV week lectures	Monotonicity, convexity and inflection points of differentiable functions, Graphing functions
XIV week exercises	Monotonicity, convexity and inflection points of differentiable functions, Graphing functions
XV week lectures	Makeup exam
XV week exercises	Makeup exam

Student workload
Per week	Per semester
8 credits x 40/30=10 hours and 40 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 4 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts Total workload for the subject: 8 x 30=240 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 48 hour(s) i 0 minuts Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations	Students are encouraged to attend classes regularly, although this is not mandatory. However, it is doubtful that one will do well in the course if you miss too many lectures.
Consultations	As agreed with the professor or teaching assistant.
Literature	1. Z. Kaldeburg, V. Mićić, S. Ognjanović, Analiza sa algebrom III, ”Krug” Beograd, 2000. 2. James Stewart, Early Transcendentals 6, ISBN-13: 978-0-495-01166-8, 2008.
Examination methods	Тhe forms of testing and grading 1. Midterm exam (up to 45 points) and Final exam (up to 45 points). 2. The points awarded for special commitment (up to 10 points). Grading scale: F (below 50 points), E (50-59 points), D (60-69), C (70-79), B (80-8
Special remarks
Comment	If opportunity to take a makeup test, or correctional final exam is used, then the results achieved on them will be treated as definitive.

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / MATHEMATICS II

Course:

MATHEMATICS II/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1311	Obavezan	2	7	3+3+0

Programs	PHYSICS
Prerequisites
Aims	The aim of the course is mastering the basics of mathematical analysis: the concept of definite and indefinite integral, multiple and functional lines.
Learning outcomes	After passing this exam, the student should be able to 1. Defines the notion of definite and indefinite integral and their connection through the Newton-Leibniz formula. 2. Find definite and indefinite integrals using techniques like substitution rule, trigonometric integration, integration by parts, integration of rational functions ... 3. Compute the area bounded by multiple curves and the volume of a solids that are obtained by revolving of that plane region about a horizontal or vertical line. 4. Uses various tests in order to determine the convergence of the series, compute Taylor's representation of certain functions. 5. Defines the basic notions and results related to the Fourier series.
Lecturer / Teaching assistant	Vladimir Božović and Dušica Slović
Methodology	Lectures, exercises, independent work, and consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	The notion of indefinite and definite integrals, Areas and distances
I week exercises	The notion of indefinite and definite integrals, Areas and distances
II week lectures	The Fundamental Theorem of Calculus, Table of elementary integrals and substitution rule
II week exercises	The Fundamental Theorem of Calculus, Table of elementary integrals and substitution rule
III week lectures	Area between two curves, Volume
III week exercises	Area between curves, Volume
IV week lectures	Integration by Parts, Trigonometric integrals, Trigonometric substitutions
IV week exercises	Integration by Parts, Trigonometric integrals, Trigonometric substitutions
V week lectures	Integration of Rational Functions by Partial Fractions, Strategy for Integrations, Approximate integrations
V week exercises	Integration of Rational Functions by Partial Fractions, Strategy for Integrations, Approximate integrations
VI week lectures	Improper integrals, Arc length and Center of mass
VI week exercises	Improper integrals, Arc length and Center of mass
VII week lectures	Series, Integral test and estimates of sums
VII week exercises	Series, Integral test and estimates of sums
VIII week lectures	Midterm exam
VIII week exercises	Midterm exam
IX week lectures	The comparison test, Alternating series
IX week exercises	The comparison test, Alternating series
X week lectures	Ratio and Root test, Strategy for testing series
X week exercises	Ratio and Root test, Strategy for testing series
XI week lectures	Power series, Representations of functions as power series
XI week exercises	Power series, Representations of functions as power series
XII week lectures	Taylor and Maclaurin series
XII week exercises	Taylor and Maclaurin series
XIII week lectures	Applications of Taylor polynomials
XIII week exercises	Applications of Taylor polynomials
XIV week lectures	Fourier series and Fourier transformation
XIV week exercises	Fourier series and Fourier transformation
XV week lectures	Makeup exam
XV week exercises	Makeup exam

Student workload
Per week	Per semester
7 credits x 40/30=9 hours and 20 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 3 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 9 hour(s) i 20 minuts x 16 =149 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 9 hour(s) i 20 minuts x 2 =18 hour(s) i 40 minuts Total workload for the subject: 7 x 30=210 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 42 hour(s) i 0 minuts Workload structure: 149 hour(s) i 20 minuts (cources), 18 hour(s) i 40 minuts (preparation), 42 hour(s) i 0 minuts (additional work)
Student obligations	Students are encouraged to attend classes regularly, although this is not mandatory. However, it is doubtful that one will do well in the course if you miss too many lectures.
Consultations	As agreed with the professor or teaching assistant.
Literature	James Stewart, Early Transcendentals 6, ISBN-13: 978-0-495-01166-8, 2008.
Examination methods	Тhe forms of testing and grading 1. Midterm exam (up to 45 points) and Final exam (up to 45 points). 2. The points awarded for special commitment (up to 10 points). Grading scale: F (below 50 points), E (50-59 points), D (60-69), C (70-79), B (80-8
Special remarks
Comment	If opportunity to take a makeup test, or correctional final exam is used, then the results achieved on them will be treated as definitive.

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / MATHEMATICS III

Course:

MATHEMATICS III/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1312	Obavezan	3	7	3+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
7 credits x 40/30=9 hours and 20 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 4 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 9 hour(s) i 20 minuts x 16 =149 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 9 hour(s) i 20 minuts x 2 =18 hour(s) i 40 minuts Total workload for the subject: 7 x 30=210 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 42 hour(s) i 0 minuts Workload structure: 149 hour(s) i 20 minuts (cources), 18 hour(s) i 40 minuts (preparation), 42 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / MATHEMATICS IV

Course:

MATHEMATICS IV/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1313	Obavezan	4	7	3+3+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
7 credits x 40/30=9 hours and 20 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 3 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 9 hour(s) i 20 minuts x 16 =149 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 9 hour(s) i 20 minuts x 2 =18 hour(s) i 40 minuts Total workload for the subject: 7 x 30=210 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 42 hour(s) i 0 minuts Workload structure: 149 hour(s) i 20 minuts (cources), 18 hour(s) i 40 minuts (preparation), 42 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / THEORETICAL ELECTRODYNAMICS

Course:

THEORETICAL ELECTRODYNAMICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1315	Obavezan	4	6	2+2+0

Programs	PHYSICS
Prerequisites	No.
Aims	To acquaint the student with the basic ideas and methods in classical electrodynamics. Special attention will be paid to clarifying the meaning of physical laws and their meaningful application. The student will also master modern mathematical formalism, notations and concepts used in theoretical physics.
Learning outcomes	Upon completion of this course the student will be able to: 1. Reproduce Maxwells and DAlemberts equations 2. Reproduce the expressions for the density and flux of the energy and momentum of the EM field, 3. Reproduce transformations of electric and magnetic fields 4. Explain the cause of electromagnetic waves 5. Explain the physical background of retarded potentials.
Lecturer / Teaching assistant	Nataša Raičević / Stevan Đurđević
Methodology	Lectures, tutorials, consultations, midterm exam, final exam.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Maxwell’s equations.
I week exercises	Introduction. A brief overview of the mastered material in electrostatics and magnetostatics.
II week lectures	Pointing’s theorem. Conservaton of momentum.
II week exercises	Tasks related to lectures from the previous and/or current week..
III week lectures	Monochromatic electromagnetic plane wave.
III week exercises	Tasks related to lectures from the previous and/or current week.
IV week lectures	Enery and momentum in electromagnetic waves. Electromagnetic waves in conductors.
IV week exercises	Tasks related to lectures from the previous and/or current week.
V week lectures	Electromagnetic wave reflection at a conducting surface. Nonmonochromatic wave.
V week exercises	Tasks related to lectures from the previous and/or current week.
VI week lectures	Scalar and vector potentials. D’Alambert equations.
VI week exercises	Tasks related to lectures from the previous and/or current week.
VII week lectures	Retarded potentials. Jefimenko’s equations.
VII week exercises	Tasks related to lectures from the previous and/or current week.
VIII week lectures	Lienard-Wiechert potentials.
VIII week exercises	Tasks related to lectures from the previous and/or current week.
IX week lectures	The field of a moving point charge.
IX week exercises	Tasks related to lectures from the previous and/or current week.
X week lectures	Electric dipole radiation.
X week exercises	Tasks related to lectures from the previous and/or current week.
XI week lectures	Midterm exam. Magnetic dipole radiation.
XI week exercises	Tasks related to lectures from the previous and/or current week.
XII week lectures	Power radiated by a point charge.
XII week exercises	Tasks related to lectures from the previous and/or current week.
XIII week lectures	Introduction to relativistic electrodynamics.
XIII week exercises	Tasks related to lectures from the previous and/or current week.
XIV week lectures	Magnetism as a relativistic phenomenon. The fields transformations.
XIV week exercises	Tasks related to lectures from the previous and/or current week.
XV week lectures	The field tensor. Electrodynamics in tensor notation. Relativistic potentials.
XV week exercises	Tasks related to lectures from the previous and/or current week.

Student workload
Per week	Per semester
6 credits x 40/30=8 hours and 0 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 4 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts Total workload for the subject: 6 x 30=180 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 36 hour(s) i 0 minuts Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to attend classes, do a midterm exam and final exam.
Consultations	Office 112 Monday: 14:00 Thursday: 14:00 Consultations can also be scheduled by email (natasar@ucg.ac.me)
Literature	1. David J. Griffiths, Introduction to electrodynamics, Prentice Hall, 1999. 2. I.V. Savelьev, Osnovi teoretičeskoй fiziki, T.1, Nauka, Moskva, 1991.(i.e. I.V. Savelyev, Fundamentals of Theoretical Physics, V. 1, Mir, Moscow, 1982.)
Examination methods	Checking and grading continuously during semester - 50 points. Final exam - 50 points. In order to pass the exam, students must earn at least 50 points.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / MATEMATICAL MODELLING

Course:

MATEMATICAL MODELLING/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
1354	Obavezan	6	5	3+1+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
5 credits x 40/30=6 hours and 40 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts Total workload for the subject: 5 x 30=150 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 30 hour(s) i 0 minuts Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / PHYSICAL MECHANICS

Course:

PHYSICAL MECHANICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
3883	Obavezan	1	8	4+3+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
8 credits x 40/30=10 hours and 40 minuts 4 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 3 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts Total workload for the subject: 8 x 30=240 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 48 hour(s) i 0 minuts Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / BASIC EXPERIMENTS I

Course:

BASIC EXPERIMENTS I/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
3884	Obavezan	1	4	2+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 1 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / LABORATORY PHYSICS I/MEHANICS/

Course:

LABORATORY PHYSICS I/MEHANICS//

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
3886	Obavezan	1	4	0+0+3

Programs	PHYSICS
Prerequisites
Aims	The aim of this course is learning the necessary skills to perform independently experiments, to analyse data and to deduce physically meaningful results. Getting acquainted with reporting the principles and the results of the performed experiment, taking into account error analysis and the reliability of the results obtained.
Learning outcomes	This training enables students to develop skills and insights into the physics experiments. This should allow them to understand, to perform and to interpret more advanced experiments, which come up in the following part.
Lecturer / Teaching assistant	prof. dr Mira Vučeljic
Methodology	Lectures and seminars with the active student participation, individual performance of experiments by student.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises	Introduction to physical experimenting
II week lectures
II week exercises	Measuring physical quantities and error estimation
III week lectures
III week exercises	Error calculations - Error and statistics
IV week lectures
IV week exercises	Data treatment - Reporting
V week lectures
V week exercises	Determination of the free fall acceleration by simple pendulum
VI week lectures
VI week exercises	Determination of the rotational inertia of a body by torsion oscillator
VII week lectures
VII week exercises	determination of the surface tension of the water…
VIII week lectures
VIII week exercises	Bernoulli's equation
IX week lectures
IX week exercises	determination of the coeficient of viscosity
X week lectures
X week exercises	determination of the elasticity coeficient
XI week lectures
XI week exercises	determination of the dancity of the liquid
XII week lectures
XII week exercises	presentations of the results of experiments that students perform independently
XIII week lectures
XIII week exercises	presentations of the results of experiments that students perform independently
XIV week lectures
XIV week exercises	presentations of the results of experiments that students perform independently
XV week lectures
XV week exercises	presentations of the results of experiments that students perform independently

Student workload	(3 hours in laboratory) per week, 15 hours in semester for consultations=60 contact hours in semester
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 0 sat(a) theoretical classes 3 sat(a) practical classes 0 excercises 2 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature	V.Vucic, Basic Measurements in Physics, Naučna knjiga, Beograd, 1984 (in Serbian). John R. Taylor, An Introduction to Error Analysis - The study of Uncertainties in Physical Measurements, Oxford University Press, ISBN 0-935702-10-5 G.L. Squires, Practic
Examination methods	Lectures and seminars with the active student participation, individual performance of experiments by student.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / BASIC EXPERIMENTS II

Course:

BASIC EXPERIMENTS II/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
3888	Obavezan	2	5	2+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
5 credits x 40/30=6 hours and 40 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts Total workload for the subject: 5 x 30=150 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 30 hour(s) i 0 minuts Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / LABORATORY PHYSICS /TERMODYNAMICS/

Course:

LABORATORY PHYSICS /TERMODYNAMICS//

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
3889	Obavezan	2	3	0+0+3

Programs	PHYSICS
Prerequisites
Aims	The aim of this course is learning the necessary skills to perform independently experiments, to analyse data and to deduce physically meaningful results. Getting acquainted with reporting the principles and the results of the performed experiment, taking into account error analysis and the reliability of the results obtained.
Learning outcomes	This training enables students to develop skills and insights in experiments in area of the mechanical waves and thermodynamics. This should allow them to understand, to perform and to interpret more advanced experiments, which come up in the following part.
Lecturer / Teaching assistant	prof. dr Mira Vučeljić
Methodology	Lectures and seminars with the active participation of students, individual performing of experiments by the student

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	This course is a continuation of the Laboratory Physics from the first semester with the experiments that cover the area of mechanical waves and thermodynamics.
I week exercises
II week lectures
II week exercises	Determination of the speed of sound from the air column
III week lectures
III week exercises	Interference of sound waves
IV week lectures
IV week exercises	Experimental checking of the Gey-Lisac low
V week lectures
V week exercises	Determination of the specific heat capacity of lead
VI week lectures
VI week exercises	Experimental checking of the Newtoon low of transfering a heat
VII week lectures
VII week exercises	Experiments in thermal expasion
VIII week lectures
VIII week exercises	Determination of the termal conductivity of glass
IX week lectures
IX week exercises	Investigation of the dependence beetwen the pressure and wather boiling temperature
X week lectures
X week exercises	Determination of the wother latent heat
XI week lectures
XI week exercises	presentations of the results of experiments that students perform independently
XII week lectures
XII week exercises	presentations of the results of experiments that students perform independently
XIII week lectures
XIII week exercises	presentations of the results of experiments that students perform independently
XIV week lectures
XIV week exercises	presentations of the results of experiments that students perform independently
XV week lectures
XV week exercises	exam

Student workload	(3 hours in laboratory) per week, 15 hours in semester for consultations=60 contact hours in semester. 30 hours – lectures with experimental work, 10 hours - seminars, 5 hours - exams, 15 hours - consultations, 30 hours – individual study
Per week	Per semester
3 credits x 40/30=4 hours and 0 minuts 0 sat(a) theoretical classes 3 sat(a) practical classes 0 excercises 1 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts Total workload for the subject: 3 x 30=90 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 18 hour(s) i 0 minuts Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature	V.Vucic, Basic Measurements in Physics, Naučna knjiga, Beograd, 1984 (in Serbian).
Examination methods	The ability for practical knowledge and skills can be tested via the interaction during the laboratory workshops. Permanent testing of the preparative knowledge and experimental skills. Periodical evaluation on the ability of the application of error anal
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ENGLISH LANGUAGE III

Course:

ENGLISH LANGUAGE III/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
4014	Obavezan	3	2	2+0+0

Programs	PHYSICS
Prerequisites	No prerequisites
Aims	The course has a goal to make students able to use English for specific purposes in the area of quantum physics
Learning outcomes	After students pass the exam they will be able to: - distinguish, understand and use complex terminology from quantum physics, - explain more complex formulas in English, - understand basic messages of popular and expert texts from the area of quantum physics in English, - have oral and written communication in English at upper intermediate level, - orally present chosen topic in English.
Lecturer / Teaching assistant	Savo Kostić
Methodology	Lectures and practice. Presentations in English on a topic studied. Studying for mid term and final exams. Consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	"Shroedinger equation", reading comprehension, discussion Grammar - countable and uncountable nouns
I week exercises
II week lectures	"Uncertainty principle", reading comprehension, discussion Grammar - expressing quantity
II week exercises
III week lectures	"Harmonic oscillator", reading comprehension, discussion Grammar - future forms
III week exercises
IV week lectures	"Quantum harmonic oscillator", reading comprehension, discussion Grammar - time clauses
IV week exercises
V week lectures	"Shroedinger equation", reading comprehension, discussion Grammar - countable and uncountable nouns
V week exercises
VI week lectures	"Mathematical formalism", reading comprehension, discussion Grammar - participles
VI week exercises
VII week lectures	Mid-term test
VII week exercises
VIII week lectures	"Hydrogen atom", reading comprehension, discussion Grammar - verb patterns
VIII week exercises
IX week lectures	"Identical particles", reading comprehension, discussion Grammar - infinitives
IX week exercises
X week lectures	"Zeeman effect", reading comprehension, discussion Grammar - modal verbs of probability
X week exercises
XI week lectures	"Zeeman effect", revision Grammar - prepositions
XI week exercises
XII week lectures	"Canonical commutators", reading comprehension, discussion Grammar - negatives and questions
XII week exercises
XIII week lectures	"Pauli matrices", reading comprehension, discussion Grammar - past and present habitual action
XIII week exercises
XIV week lectures	"Angular momentum", reading comprehension, discussion Grammar - real and unreal time
XIV week exercises
XV week lectures	Preparation for the final exam
XV week exercises

Student workload	2 classes, 45 minutes each
Per week	Per semester
2 credits x 40/30=2 hours and 40 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 0 excercises 0 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 2 hour(s) i 40 minuts x 16 =42 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 2 hour(s) i 40 minuts x 2 =5 hour(s) i 20 minuts Total workload for the subject: 2 x 30=60 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 12 hour(s) i 0 minuts Workload structure: 42 hour(s) i 40 minuts (cources), 5 hour(s) i 20 minuts (preparation), 12 hour(s) i 0 minuts (additional work)
Student obligations	Students need to regularly attend classes, make a presentation and take a mid term and a final exam.
Consultations	once a week for 2 hours
Literature
Examination methods	English for Physics, reader Oxford Upper Intermediate, Liz and John Soars with Jo Devoy
Special remarks	Classroom language is English
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ENGLISH LANGUAGE IV

Course:

ENGLISH LANGUAGE IV/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
4015	Obavezan	4	2	2+1+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
2 credits x 40/30=2 hours and 40 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises -1 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 2 hour(s) i 40 minuts x 16 =42 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 2 hour(s) i 40 minuts x 2 =5 hour(s) i 20 minuts Total workload for the subject: 2 x 30=60 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 12 hour(s) i 0 minuts Workload structure: 42 hour(s) i 40 minuts (cources), 5 hour(s) i 20 minuts (preparation), 12 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / COMPLEX ANALYSIS

Course:

COMPLEX ANALYSIS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
4290	Obavezan	4	4	2+1+0

Programs	PHYSICS
Prerequisites	Analysis I
Aims	Students will get acquaintance with basic notions of theory of complex analysis with emphasizes on applications in physics.
Learning outcomes	After passing this exam, a student: Applies basic operations within the field of complex numbers Generalizes elementary real functions (og, sin, cos, exp, ...) in a complex framework Calculates the sum of real lines using complex functions It is located a copy of the integral of complex functions Develops functions Taylor and Laurent series Mapping complex field by holomorphic functions
Lecturer / Teaching assistant	Darko Mitrović
Methodology	Lectures, practical problems, homework, written and oral tests. Consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Set of complex numbers. Operations in the set.
I week exercises	Set of complex numbers. Operations in the set.
II week lectures	Sequence of complex numbers, its convergence, and basic properties
II week exercises	Sequence of complex numbers, its convergence, and basic properties
III week lectures	Functions of complex variables. Inverse functions. Limit of functions.
III week exercises	Functions of complex variables. Inverse functions. Limit of functions.
IV week lectures	Continuity of functions
IV week exercises	Continuity of functions
V week lectures	Basic transcendent functions. Euler formula.
V week exercises	Basic transcendent functions. Euler formula.
VI week lectures	Derivative of complex function. Riemann conditions. Harmonic functions
VI week exercises	Derivative of complex function. Riemann conditions. Harmonic functions
VII week lectures	Integral of complex function. Cauchy theorem.
VII week exercises	Integral of complex function. Cauchy theorem.
VIII week lectures	Definite integral. Integral along closed curvature. Cauchy integral formula.
VIII week exercises	preparation for I colloquium
IX week lectures	I colloquium
IX week exercises	preparation for correction of I colloquium
X week lectures	Correction of I colloquium
X week exercises	Defence of homework
XI week lectures	Conformal mappings. Linear and rational functions.
XI week exercises	Conformal mappings. Linear and rational functions.
XII week lectures	Exponential function. Trigonometric function. Functional series.
XII week exercises	Exponential function. Trigonometric function. Functional series.
XIII week lectures	Taylor series. Laurent series.
XIII week exercises	preparation for II colloquium
XIV week lectures	II coloquium.
XIV week exercises	preparation for correction of II colloquium
XV week lectures	Isolated singularities. Laurent expansion.
XV week exercises	Correction of II colloquium.

Student workload	5.3 hours
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 2 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations	Lectures, practical problems, homework, written and oral tests. Consultations.
Consultations	1 hour/week
Literature	V. Dajović: Teorija funkcija kompleksne promjenljive; M. Ušćumlić, P. Miličić: Zbirka zadataka iz Matematike.
Examination methods	1 homewor for 5 points; Two colloquium 40 points each; Attending lectures 5 points; Final exam 10 points. Success limit is 50 points
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / INTRODUCTION TO NUCLEAR PHYSICS

Course:

INTRODUCTION TO NUCLEAR PHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
4304	Obavezan	6	6	3+3+0

Programs	PHYSICS
Prerequisites
Aims	The overall goal of the course is to introduce students with basics of nuclear physics, i.e. basic properties of the atomic nucleus, nuclear forces, some nuclear models, radioactivity and nuclear reactions.
Learning outcomes	Upon successful completion of the course students will be able to: state and basically explain the properties of the atomic nucleus and nuclear forces; calculate and interpret quantities characterizing the nuclide; distinguish among isotopes, isotones and isobars; apply quantum mechanics and electrodynamics in a description of the nuclear electromagnetic moments; understand basics of the nucleon-nucleon interaction and simple nuclear models; apply the laws of radioactive decay – in theoretical analyzes and simple experiments; define conservation laws valid in radioactive transformations and nuclear reactions.
Lecturer / Teaching assistant	Prof Dr Nevenka Antović and Dr Krsto Ivanović
Methodology	Lectures, exercises, homework, seminar paper, consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Properties of stable nuclei, nature and characteristics of nuclear forces. A and Z. Mass of nucleons and nucleus.
I week exercises	Mass number and nuclear charge.
II week lectures	Nuclear binding energy and nuclear stability.
II week exercises	Nuclear binding energy.
III week lectures	Semi-empirical mass formula. Nuclear radius.
III week exercises	Mass of the nucleus. Nuclear radius.
IV week lectures	Spin and magnetic moment of nucleons and nucleus.
IV week exercises	Spin and magnetic moment of the nucleus.
V week lectures	Electric quadrupole moment. Parity. Isospin.
V week exercises	Electric quadrupole moment. Parity. Isospin.
VI week lectures	Midterm exam I
VI week exercises	Midterm exam I
VII week lectures	Nucleon-nucleon interaction: forces and potentials. Deuteron.
VII week exercises	Nucleon-nucleon interaction.
VIII week lectures	Basics of the meson theory of nuclear forces.
VIII week exercises	Nucleon-nucleon interaction – cont.
IX week lectures	Nuclear models: the liquid-drop model, the Fermi gas model.
IX week exercises	The liquid-drop model, the Fermi gas model.
X week lectures	The shell model – experimental basis, construction principles, schemes, experimental consequences, limitations.
X week exercises	The shell model.
XI week lectures	Single-particle states (non-spherical potential). Rotational states.
XI week exercises	Single-particle states. Rotational states.
XII week lectures	Midterm exam II
XII week exercises	Midterm exam II
XIII week lectures	Vibration levels. Resonances. Application of the collective model.
XIII week exercises	Vibration levels. Resonances.
XIV week lectures	Radioactive decay (nuclear instabilities, decay laws).
XIV week exercises	The law of radioactive decay.
XV week lectures	General laws and types of nuclear reactions: classification, conservation laws; nuclear fission and fusion.
XV week exercises	Nuclear reactions – conservation laws.

Student workload	Weekly: 6 x 40/30 = 8 h; total: 6 x 30 = 180 h.
Per week	Per semester
6 credits x 40/30=8 hours and 0 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 2 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts Total workload for the subject: 6 x 30=180 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 36 hour(s) i 0 minuts Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations	Regular attendance, homework, seminar paper, two midterm exams and final exam.
Consultations	After lectures and exercises.
Literature	K. N. Mukhin, Experimental Nuclear Physics. Volume I: Physics of Atomic Nucleus, Mir Publishers, Moscow, 1987 (in Russian: К. Н. Мухин, Экспериментальная ядерная физика: Физика атомного ядра, Энергоатомиздат, Москва, 1983); K. S. Krane, Introductory Nuclear Physics, John Wiley & Sons, New York, 1988; M. Krmar, Introduction to Nuclear Physics, University of Novi Sad, Novi Sad, 2013 (in Serbian); L. Marinkov, Basis of Nuclear Physics, University of Novi Sad, Novi Sad, 2010 (in Serbian); D. Krpić, I. Aničin, I. Savić, Nuclear physics through tasks, University of Belgrade, Belgrade, 1996 (in Serbian).
Examination methods	Regular attendance: 4 points; homework: 4 points (2 x 2); seminar paper: 12 points; midterm exams: 40 points (2 x 20); final exam: 40 points. A minimum of 50 points is required for successful completion of the course.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / LABORATORY PHYSICS /NUCLEAR PHYSICS/ III

Course:

LABORATORY PHYSICS /NUCLEAR PHYSICS/ III/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
4308	Obavezan	6	3	0+0+3

Programs	PHYSICS
Prerequisites
Aims	Introducing students with simple instruments and methods in nuclear physics (particularly in spectroscopy and dosimetry of radiation) and data analysis, together with the development of their skills in designing and conducting experiments, as well as in undertaking radiation protection measures.
Learning outcomes
Lecturer / Teaching assistant	Nevenka Antović / Vanja Veljović
Methodology	Introductory lectures, experiments, seminar paper, consultations.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Introduction: Types and sources of radiation.
I week exercises
II week lectures	Interaction of radiation with matter. Radiation protection – principles and measures.
II week exercises
III week lectures	Theoretical introduction to the data analysis, instruments and methods that will be used in the practicum.
III week exercises
IV week lectures	Entrance test
IV week exercises
V week lectures
V week exercises	Statistical fluctuation in nuclear processes.
VI week lectures
VI week exercises	Characteristics of the Geiger-Muller counter.
VII week lectures
VII week exercises	Determination of gamma-ray energy by absorption in Pb.
VIII week lectures
VIII week exercises	Determination of maximum energy of beta-rays by absorption in Al.
IX week lectures
IX week exercises	Determination of alpha-particles energy with nuclear emulsion.
X week lectures
X week exercises	Measurement of background radiation – indoor and outdoor.
XI week lectures
XI week exercises	Radon measurement – RAD7.
XII week lectures	Radiation doses. ALARA principle.
XII week exercises	Measuring and dose rate evaluation.
XIII week lectures
XIII week exercises	Decontamination of working table in the lab.
XIV week lectures	Seminar papers
XIV week exercises
XV week lectures	Application of radiation sources in industry and medicine. Radiation protection – international recommendations and standards.
XV week exercises

Student workload	3 x 40/30 = 4 hours per week. Total: 3 x 30 = 90 hours.
Per week	Per semester
3 credits x 40/30=4 hours and 0 minuts 0 sat(a) theoretical classes 3 sat(a) practical classes 0 excercises 1 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts Total workload for the subject: 3 x 30=90 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 18 hour(s) i 0 minuts Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations	Regular attendance, entrance test, experimental exercises and results presentation, final report on experiments, seminar paper and final exam.
Consultations	As agreed with lecturer.
Literature	I. Draganić, Radioactive isotopes and radiations – books I, II and III, Naučna knjiga and University of Belgrade and Institute Vinča, Belgrade, 1962/3, 1968, 1981 (in Serbian); Written (lecturer’s) instructions for laboratory exercises in nuclear physics.
Examination methods	Regular attendance: 4 points; entrance test: 30 points; seminar paper: 10 points; experimental exercises successfully performed: 8 x 2 points (16 points); final exam: 40 points. Passing grades: E (51-59), D (60-69), C (70-79), B (80-89), A (90-100).
Special remarks	The condition for the start of experimental exercises: at least 15 points from the entrance test.
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / BASICS OF PHYSICS MEASUREMENTS TECHNIQUES I

Course:

BASICS OF PHYSICS MEASUREMENTS TECHNIQUES I/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
4938	Obavezan	3	4	2+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 1 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / BASICS OF PHYSICS MEASUREMENTS TECHNIQUES II

Course:

BASICS OF PHYSICS MEASUREMENTS TECHNIQUES II/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
4939	Obavezan	4	4	2+2+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 1 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / LABORATORY PHYSICS /ELECTROMAGNETISM/

Course:

LABORATORY PHYSICS /ELECTROMAGNETISM//

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
5512	Obavezan	3	3	0+0+3

Programs	PHYSICS
Prerequisites	None.
Aims	To provide the student with experience in physics experiments and enhance their ability and familiarity with related equipment and techniques. To complement and reinforce the theory covered in lecture modules, and in so doing, demonstrating to the student the important synergy of classroom and laboratory teaching in science education. To provide the student with training in the following areas: (i) good laboratory practice. (ii) keeping a laboratory notebook. (iii) data analysis and presentation. (iv) technical report writing. (v) appropriate aspects of laboratory safety. To enhance the practical skills of the student in performing experiments involving a wide range of physical concepts.
Learning outcomes	Students will know good procedures for carrying out an experiment. Students will know how to keep a good laboratory notebook and how to present a written scientific report, and appreciate the importance of these activities in relation to teaching in a secondary school. Students will develop a more critical analytical ability in evaluating data. Students will become aware of the physics experiments used in the secondary school physics curricula, the equipment required, and appropriate aspects of its correct use and maintenance. Students will develop an appreciation of the important complementary nature of classroom and laboratory teaching for science education.
Lecturer / Teaching assistant	Prof. dr Ivana Pićurić mr Vanja Veljović
Methodology	Lectures and seminars with the active student participation, individual performance of experiments by student.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises	Introduction. A range of short experiments of Electromagneism, which illustrate concepts from lectures. Measuring methods, techniques and instruments.
II week lectures
II week exercises	Ohm’s law in DC circuits. Internal resistance of a source of EMS.
III week lectures
III week exercises	The Wheatstone Bridge. Resistors connected in parallel and series. Kirchhoff 's curent laws.
IV week lectures
IV week exercises	Temperature coefficient of resistance.
V week lectures
V week exercises	Faraday’s law of eleclrolysis, electrochemisal Cu equivalent.
VI week lectures
VI week exercises	Presentations of the results of experiments that students perform independently.
VII week lectures
VII week exercises	Thermoelectric cell couple.
VIII week lectures
VIII week exercises	Ohm’s law in AC circuits. A resistor, an inductor and a capacitive element in AC circuit. The single loop RLC circuit.
IX week lectures
IX week exercises	RC circuits. Discharging a capacitor.
X week lectures
X week exercises	Joule’s law of heating.
XI week lectures
XI week exercises	Presentations of the results of experiments that students perform independently.
XII week lectures
XII week exercises	Presentations of the results of experiments that students perform independently.
XIII week lectures
XIII week exercises	Presentations of the results of experiments that students perform independently.
XIV week lectures
XIV week exercises	Presentations of the results of experiments that students perform independently.
XV week lectures
XV week exercises	Laboratory exam.

Student workload	Per week: 3 ECTS x 40/30 = 4 hours Laboratories: 3 hours Individual study: 1 hour.
Per week	Per semester
3 credits x 40/30=4 hours and 0 minuts 0 sat(a) theoretical classes 3 sat(a) practical classes 0 excercises 1 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts Total workload for the subject: 3 x 30=90 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 18 hour(s) i 0 minuts Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature	V. Vucic: Osnovna merenja u fizici. Naućna knjiga, Beograd.
Examination methods	Laboratory exam 44 points and estimation of individual activity on lectures and laboratory notebook 7 points each laboratory experiment (max 56 points). Passing grade is obtained if the cumulative collected at least 51 points.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / LABORATORY PHYSICS II /OPTICS/

Course:

LABORATORY PHYSICS II /OPTICS//

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
5513	Obavezan	4	3	0+0+3

Programs	PHYSICS
Prerequisites
Aims	To provide the student with experience in physics experiments and enhance their ability and familiarity with related equipment and techniques. To complement and reinforce the theory covered in lecture modules, and in so doing, demonstrating to the student the important synergy of classroom and laboratory teaching in science education. To provide the student with training in the following areas: (i) good laboratory practice. (ii) keeping a laboratory notebook. (iii) data analysis and presentation. (iv) technical report writing. (v) appropriate aspects of laboratory safety. To enhance the practical skills of the student in performing experiments involving a wide range of physical concepts.
Learning outcomes	Students will know good procedures for carrying out an experiment. Students will know how to keep a good laboratory notebook and how to present a written scientific report, and appreciate the importance of these activities in relation to teaching in a secondary school. Students will develop a more critical analytical ability in evaluating data. Students will become aware of the physics experiments used in the secondary school physics curricula, the equipment required, and appropriate aspects of its correct use and maintenance. Students will develop an appreciation of the important complementary nature of classroom and laboratory teaching for science education.
Lecturer / Teaching assistant	professor dr Ivana Pićurić – Teacher; Physicist Vanja Veljović - senior laboratory assistant.
Methodology	Lectures and seminars with the active student participation, individual performance of experiments by student.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises	Introduction. A range of short experiments of Optics, which illustrate concepts from lectures. Measuring methods, techniques and instruments.
II week lectures
II week exercises	The preparation for the laboratory experiments.
III week lectures
III week exercises	Determination of the focal length of lens.
IV week lectures
IV week exercises	Microscope.
V week lectures
V week exercises	Diffraction gratings. The wavelength of the He-Ne laser in Fresnel difraction.
VI week lectures
VI week exercises	The Spectral Analysis.
VII week lectures
VII week exercises	Polarization of the He-Ne laser's light.
VIII week lectures
VIII week exercises	Polarization with optically active material.
IX week lectures
IX week exercises	Index of refraction. Angle of minimum deviation.
X week lectures
X week exercises	Determination of the colored solutions concentration using a colorimeter.
XI week lectures
XI week exercises	Presentations of the results of experiments that students perform independently.
XII week lectures
XII week exercises	Presentations of the results of experiments that students perform independently.
XIII week lectures
XIII week exercises	Presentations of the results of experiments that students perform independently.
XIV week lectures
XIV week exercises	Presentations of the results of experiments that students perform independently.
XV week lectures
XV week exercises	Laboratory exam.

Student workload	Per week: 3 ECTS x 40/30 = 4 hours Laboratories: 3 hours Individual study: 1 hour.
Per week	Per semester
3 credits x 40/30=4 hours and 0 minuts 0 sat(a) theoretical classes 3 sat(a) practical classes 0 excercises 1 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts Total workload for the subject: 3 x 30=90 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 18 hour(s) i 0 minuts Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature	V. Vucic: Osnovna merenja u fizici. Naućna knjiga, Beograd.
Examination methods	Laboratory exam 44 points and estimation of individual activity on lectures and laboratory notebook 7 points each laboratory experiment (max 56 points). Passing grade is obtained if the cumulative collected at least 51 points.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / QVANTUM MECHANICS I

Course:

QVANTUM MECHANICS I/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
7489	Obavezan	5	8	3+2+0

Programs	PHYSICS
Prerequisites	Classical mechanics
Aims	Introduction to the basic laws of physics that apply at the level of atoms and their nuclei
Learning outcomes	Upon completion of this course the student will be able to: 1. know how to solve the simplest examples of one-dimensional Schrödinger equation 2. understand the statistical interpretation of wave function and measurement 3. interpret the uncertainty relation 4. know the basic properties of momentum in quantum mechanics 5. reproduce basic properties spectra of hydrogen atoms
Lecturer / Teaching assistant	Prof. dr Predrag Miranović, lecturer; mr Stevan Đurđević, assistant
Methodology	lectures, exercises, consultations

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Wave function. Schrödinger equation. Statistical interpretation. Probability.
I week exercises
II week lectures	Normalization
II week exercises
III week lectures	Momentum. Uncertainty principle
III week exercises
IV week lectures	Time independent Schrödinger equation. Stationary states.
IV week exercises
V week lectures	Infinite square well
V week exercises
VI week lectures	Harmonic oscillator
VI week exercises
VII week lectures	Finite depth potential well
VII week exercises
VIII week lectures	Free particle
VIII week exercises
IX week lectures	Delta-function potential
IX week exercises
X week lectures	Mathematical formalism. Linear algebra
X week exercises
XI week lectures	Hilbert space. Generalized statistical interpretation
XI week exercises
XII week lectures	Schrödinger and Heisenberg picture
XII week exercises
XIII week lectures	Quantum mechanics in three dimensions. Schrödinger equation in spherical coordinates
XIII week exercises
XIV week lectures	Hydrogen atom
XIV week exercises
XV week lectures	Angular momentum
XV week exercises

Student workload
Per week	Per semester
8 credits x 40/30=10 hours and 40 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 5 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts Total workload for the subject: 8 x 30=240 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 48 hour(s) i 0 minuts Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to attend classes regularly.
Consultations	Every week on request
Literature	1. Introduction to quantum mechanics, D. J. Griffiths, Prentice Hall, New Jersey 2005
Examination methods	Tests (40 points), homework (10 points), final exam (50 points).
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / WAVES AND THERMOPHISICS

Course:

WAVES AND THERMOPHISICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
8607	Obavezan	2	10	4+4+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
10 credits x 40/30=13 hours and 20 minuts 4 sat(a) theoretical classes 0 sat(a) practical classes 4 excercises 5 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 13 hour(s) i 20 minuts x 16 =213 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 13 hour(s) i 20 minuts x 2 =26 hour(s) i 40 minuts Total workload for the subject: 10 x 30=300 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 60 hour(s) i 0 minuts Workload structure: 213 hour(s) i 20 minuts (cources), 26 hour(s) i 40 minuts (preparation), 60 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / OSCILLATIONS AND WAVES

Course:

OSCILLATIONS AND WAVES/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
10107	Obavezan	2	5	2+2+0

Programs	PHYSICS
Prerequisites	None
Aims	Acquiring knowledge from the basics of mechanical oscillations and waves, acquiring operational knowledge from methods of solving physical problems, skills in reducing a real problem from mechanical oscillations and waves to a physical model and setting up appropriate equations.
Learning outcomes	After the student passes this exam, he will be able to: develop a simple physical model applicable to the solution of the given problem, set up a mathematical formulation of the given physical model, solve numerical tasks from oscillations and waves for known systems, quantitatively and qualitatively describe damping and forcing in systems that behave like a harmonic oscillator, knows the basic concepts of the creation and propagation of waves, knows the phenomena of reflection, transparency and interference of waves.
Lecturer / Teaching assistant	prof. dr Gordana Jovanovic
Methodology	Lectures and calculus exercises, consultations, colloquium, remedial colloquium and final exam.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	A simple harmonic oscillator. Harmonic oscillations. Examples.
I week exercises	A simple harmonic oscillator. Harmonic oscillations. Examples.
II week lectures	Harmonic oscillator energy. Examples for a simple harmonic oscillator.
II week exercises	Harmonic oscillator energy. Examples for a simple harmonic oscillator.
III week lectures	Free oscillation of a single body in complex systems. Longitudinal and transverse oscillation. The principle of superposition. Amplitude modulation.
III week exercises	Free oscillation of a single body in complex systems. Longitudinal and transverse oscillation. The principle of superposition. Amplitude modulation.
IV week lectures	Damped oscillation of the mechanical system.
IV week exercises	Damped oscillation of the mechanical system.
V week lectures	Forced oscillation of a mechanical system.
V week exercises	Forced oscillation of a mechanical system.
VI week lectures	Waves in one dimension - generation and propagation through an elastic medium. Wave function of plane and spherical wave; phase velocity.
VI week exercises	Waves in one dimension - generation and propagation through an elastic medium. Wave function of plane and spherical wave; phase velocity.
VII week lectures	The wave equation. Velocity of plane waves in a solid elastic medium.
VII week exercises	The wave equation. Velocity of plane waves in a solid elastic medium.
VIII week lectures	Energy of mechanical waves. Wave intensity.
VIII week exercises	Energy of mechanical waves. Wave intensity.
IX week lectures	Colloquium.
IX week exercises	Colloquium.
X week lectures	Reflection and refraction of waves. Coefficients of reflection and transparency. Wave resistance.
X week exercises	Reflection and refraction of waves. Coefficients of reflection and transparency. Wave resistance.
XI week lectures	Wave interference.
XI week exercises	Wave interference.
XII week lectures	Standing waves. Waves in multiple dimensions. Wave polarization.
XII week exercises	Standing waves. Waves in multiple dimensions. Wave polarization.
XIII week lectures	Sound. Sound characteristics. Sound sources. Oscillation of string and stick.
XIII week exercises	Sound. Sound characteristics. Sound sources. Oscillation of string and stick.
XIV week lectures	Oscillation of air columns. Speed of sound.
XIV week exercises	Oscillation of air columns. Speed of sound.
XV week lectures	Sound intensity. Ultrasound. Doppler effect.
XV week exercises	Sound intensity. Ultrasound. Doppler effect.

Student workload	Weekly 5,5h=1,5h lectures+1,5h exercises+2,5h independent work including consultations In the semester 5,5hx15=82,5h
Per week	Per semester
5 credits x 40/30=6 hours and 40 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts Total workload for the subject: 5 x 30=150 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 30 hour(s) i 0 minuts Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations	Attending lectures and calculus exercises, consultations, preparation of the colloquium (40 points) and final exam (60 points).
Consultations	agreement with students
Literature	S. Backović, Physical Mechanics, Institute for Textbooks and Teaching Aids, Podgorica 1999. D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, John Wiley&Sons, 2005 I. Irodov, A collection of problems in general physics, Institute for Textbooks and Teaching Aids, Podgorica 2000.
Examination methods	A colloquium worth 40 points and a final exam worth 60 points. The minimum number of points to pass the exam is 51.
Special remarks	none
Comment	Classes are held for a group of about 10 students.

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / MOLECULAR PHYSICS AND THERMODYNAMICS

Course:

MOLECULAR PHYSICS AND THERMODYNAMICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
10108	Obavezan	2	7	3+3+0

Programs	PHYSICS
Prerequisites
Aims	Acquiring knowledge about thermal phenomena, processes and laws, as well as about the basic relations and principles of the molecular-kinetic theory of gases and thermodynamics.
Learning outcomes	After successful completion of the course students should be able to: understand basic concept of heat transfer and interpret different heat transfer mechanisms (conduction, convection, radiation); explain “behavior“ of molecules and relevant distributions, demonstrate knowledge of the ideal gas model, derive the van der Waals equation and apply it to a real gas; use thermodynamic terminology correctly, derive and discuss the first and second laws of thermodynamics, analyze basic thermodynamic cycles, distinguish between thermodynamic potentials, understand the concept of thermodynamic equilibrium; develop a simple physical model applicable to solving a given problem from the molecular-kinetic theory and thermodynamics; describe in general phenomena at the boundary of different phases, phase transitions and phase diagram.
Lecturer / Teaching assistant	Prof Dr Nevenka Antović, Dr Krsto Ivanović
Methodology	Lectures, exercises, consultations, homework.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Thermal and molecular properties of matter. Temperature and temperature scales. Thermal expansion.
I week exercises	Temperature scales. Thermal expansion.
II week lectures	Thermal stress. Quantity of heat. Heat transfer.
II week exercises	Thermal stress. Quantity of heat. Heat transfer (conduction).
III week lectures	Specific heats. Basics of calorimetry. Kinetic theory of gases – basic relations.
III week exercises	Heat transfer (convection, radiation). Specific heats.
IV week lectures	Ideal gas – equation of state, processes, work. Internal energy and degrees of freedom.
IV week exercises	Basic relations of the kinetic theory of gases. Ideal gas – equation of state.
V week lectures	Mean free path. Maxwell and Boltzmann distribution.
V week exercises	Ideal gas – processes, work; mean free path; Maxwell and Boltzmann distribution.
VI week lectures	Midterm exam I
VI week exercises	Midterm exam I
VII week lectures	Real gas – equation of state, internal energy. Joule-Thomson effect.
VII week exercises	Van der Waals equation; real gas – internal energy.
VIII week lectures	Viscosity, thermal conductivity and diffusion of gases. Properties of ultra-dilute gases.
VIII week exercises	Viscosity, thermal conductivity and diffusion of gases.
IX week lectures	Thermodynamic system; state. Thermodynamic process. Laws of thermodynamics.
IX week exercises	Laws of thermodynamics.
X week lectures	Heat engine; refrigerator. Carnot and other cycles. Clausius inequality.
X week exercises	Thermodynamic cycles.
XI week lectures	Entropy. Nernst theorem. Thermodynamic potentials.
XI week exercises	Thermodynamic cycles. Entropy. TS-diagram.
XII week lectures	Surface tension; force. Phenomena at the boundary between phases. Capillarity.
XII week exercises	Midterm exam II
XIII week lectures	Phase transitions. Evaporation and condensation. Ideal and real isotherms; critical point.
XIII week exercises	Surface tension; capillary action.
XIV week lectures	Metastable states of vapor and liquid. Clausius-Clapeyron equation.
XIV week exercises	Evaporation and condensation. Clausius-Clapeyron equation.
XV week lectures	Melting and crystallization. Equilibrium conditions between phases. Triple point – phase diagram.
XV week exercises	Melting and crystallization. Phase diagram.

Student workload	Weekly: 7 x 40/30 = 9 h and 20 min; total: 7 x 30 = 210 h
Per week	Per semester
7 credits x 40/30=9 hours and 20 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 3 excercises 3 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 9 hour(s) i 20 minuts x 16 =149 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 9 hour(s) i 20 minuts x 2 =18 hour(s) i 40 minuts Total workload for the subject: 7 x 30=210 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 42 hour(s) i 0 minuts Workload structure: 149 hour(s) i 20 minuts (cources), 18 hour(s) i 40 minuts (preparation), 42 hour(s) i 0 minuts (additional work)
Student obligations	Attending classes (lectures and exercises) regularly; doing homework assignments and taking midterm exams.
Consultations	As needed.
Literature	D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, John Wiley&Sons, 2005; B. Žižić, Kurs opšte fizike – Molekularna fizika, termodinamika, mehanički talasi. IRO Građevinska knjiga, Beograd, 1988; I. Irodov, Zbirka zadataka iz opšte fizike, Zavod za udžbenike i nastavna sredstva, Podgorica, 2000; G. Dimić, M. Mitrinović, Zbirka zadataka iz fizike (kurs D), Naša knjiga, Beograd, 2000.
Examination methods	Regular attendance: 5 points; homework: 5 points (5 x 1); midterm exams: 40 points (2 x 20); final exam: 50 points. In order to pass the course, students have to achieve at least 50 points.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / THEORETICAL MECHANICS AND SPEC. THEORY OF RELATIV.

Course:

THEORETICAL MECHANICS AND SPEC. THEORY OF RELATIV./

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
10163	Obavezan	3	6	3+2+0

Programs	PHYSICS
Prerequisites	Classical mechanics
Aims	The goal of this course is to reformulate the physical laws that the student learned in Classical Mechanics by deriving them from general principles that go beyond the limits of Classical Mechanics.
Learning outcomes	After completing this course, the student will be able to: 1. Explain the principle of minimum action 2. set Lagranges equations for the simplest forms of one-dimensional motion 3. set the basic formulas of relativistic kinematics and dynamics 4. explain the dilation of time and space 5. explain the laws of conservation based on the properties of space and time
Lecturer / Teaching assistant	Professor Predrag Miranovic, assistant Stevan Đurđević
Methodology	Lectures, exercises, consultations

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Introduction. Connections. Dalambers principle
I week exercises
II week lectures	Lagranges equations
II week exercises
III week lectures	Lagrangian function and energy
III week exercises
IV week lectures	The principle of minimum action
IV week exercises
V week lectures	Law of conservation of energy, momentum and momentum of momentum
V week exercises
VI week lectures	Motion of a particle in a central field
VI week exercises
VII week lectures	Particle scattering
VII week exercises
VIII week lectures	Small oscillations
VIII week exercises
IX week lectures	Rigid body kinematics. Euler angles. Tensor of inertia
IX week exercises
X week lectures	Moment of impulse of a rigid body. Free axes of rotation.
X week exercises
XI week lectures	Eulers equations
XI week exercises
XII week lectures	Hamiltons equations. Poisson brackets. Hamilton-Jacobi equations
XII week exercises
XIII week lectures	The special theory of relativity
XIII week exercises
XIV week lectures	Relativistic kinematics
XIV week exercises
XV week lectures	Relativistic dynamics
XV week exercises

Student workload
Per week	Per semester
6 credits x 40/30=8 hours and 0 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 2 excercises 3 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts Total workload for the subject: 6 x 30=180 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 36 hour(s) i 0 minuts Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to attend lectures and exercises
Consultations	Every week upon request
Literature	Clasical mechanics, H. Goldstein, C. Poole, J. Safko, Addison Wesley 2000
Examination methods	Tests (40 points), Homework (10 points), Final exam (50 points)
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / INTRODUCTION TO ATOMIC PHYSICS

Course:

INTRODUCTION TO ATOMIC PHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
10164	Obavezan	4	4	2+1+0

Programs	PHYSICS
Prerequisites	None
Aims	The course Introduction to Atomic Physics aims to introduce students to the physics of the microcosm and introduce them to the basic experimental facts on which it rests, as well as to the corresponding theory in its historical development and application.
Learning outcomes	After passing the exam, the student will be able to explain the essence of the process from the basic areas of atomic physics and to use scientific and professional literature.
Lecturer / Teaching assistant	prof. dr. Mara Šćepanović
Methodology	Lectures, calculus exercises, control tests, colloquiums, seminar papers, consultations, constant checking of knowledge through oral examination, independent study and homework.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	Preparation and registration of the semester.A detailed presentation of the plan for the organization of lectures and exams. Atomic structure of matter,
I week exercises	Selected tasks accompanying the lectures
II week lectures	Determination of mass and charge of a particle, division of the first seminar paper,
II week exercises	Selected tasks accompanying the lectures
III week lectures	Determination of mass and charge of particles (continued), first control test
III week exercises	Selected tasks accompanying the lectures
IV week lectures	Corpuscular properties of electromagnetic waves oral examination,
IV week exercises	Selected tasks accompanying the lectures
V week lectures	Corpuscular properties of electromagnetic waves (continued), oral examination, second control test.
V week exercises	Selected tasks accompanying the lectures
VI week lectures	Corpuscular properties of electromagnetic waves (continued), oral examination,
VI week exercises	Selected tasks accompanying the lectures
VII week lectures	First colloquium, presentation of the first seminar paper
VII week exercises	Insight into the works, discussion of the results so far
VIII week lectures	Wave properties of corpuscles, oral examination; distribution of the second seminar paper, the third control test
VIII week exercises	Selected tasks accompanying the lectures
IX week lectures	Wave properties of bodies (continued), oral examination,
IX week exercises	Selected tasks accompanying the lectures
X week lectures	Wave properties of corpuscles (continued), oral examination, fourth control test,
X week exercises	Selected tasks accompanying the lectures
XI week lectures	Discretion of atomic states oral examination,
XI week exercises	Selected tasks accompanying the lectures
XII week lectures	Discretion of atomic states, oral exam; fifth control test,
XII week exercises	Selected tasks accompanying the lectures
XIII week lectures	Discretion of atomic states (continued), oral examination
XIII week exercises	Selected tasks accompanying the lectures
XIV week lectures	Sixth control test; presentation of the second seminar paper
XIV week exercises	presentation of the second seminar paper, continued
XV week lectures	Second colloquium
XV week exercises	Insight into the works, discussion of the results so far

Student workload	per week 4 credits x 40/30≈5 hours and 20 minutes Structure: 2 hours of lectures, 1 hour of calculation exercises, 2 hours and 20 minutes of independent work including consultations, In the semester Classes and final exam: 5 hours and 20 minutes x 16≈85 hours and 30 minutes; Necessary preparations before the beginning of the semester (administration, registration, certification): 2x5 hours and 20 minutes = 10 hours and 40 minutes; Total course load: 4h30=120 hours Additional work on exam preparation in the remedial period, including taking the remedial exam, is from 0 to 23 hours and 50 minutes. Load structure: 85 hours and 30 minutes (teaching) + 10 hours and 40 minutes (preparation) + 23 hours and 50 minutes (additional work)
Per week	Per semester
4 credits x 40/30=5 hours and 20 minuts 2 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 2 hour(s) i 20 minuts of independent work, including consultations	Classes and final exam: 5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts Total workload for the subject: 4 x 30=120 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 24 hour(s) i 0 minuts Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations	Students are required to regularly attend classes, pass all control tests, both colloquiums, and do and defend seminar papers. If, for any reason, a student misses two periods of lectures and exercises (in total) and if he does not complete all tests and seminar work by the first colloquium, he will be prohibited from taking the exam. The same rule with the same ban applies to the period up to the second colloquium.
Consultations	Consultations are held at the request of students, usually after exercises
Literature	C. J. Joachain; Physics of Atoms and Molecules Foot; Atomic Physics
Examination methods	Six control tests with a total of 24 points (up to 4 points for each successfully completed test); Two seminar papers with a total of 16 points (up to 8 points for each successfully defended paper); Two colloquiums with a total of 30 points (up to 15 points for each successfully completed colloquium); Exam up to 30 points. A passing grade is obtained if a total of 51 points is collected
Special remarks	Classes can also be organized in English
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / INTRODUCTION TO ASTRONOMY AND ASTROPHYSICS

Course:

INTRODUCTION TO ASTRONOMY AND ASTROPHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
10167	Obavezan	6	6	3+0+0

Programs	PHYSICS
Prerequisites	none
Aims	The course Introduction to Astronomy and Astrophysics aims to acquaint students with basic cosmological concepts and enable them to acquire general and specific knowledge in astronomy and astrophysics.
Learning outcomes	After passing the exam, the student will be able to master the basic concepts and knowledge of astronomy and astrophysics, know the basic physical laws and understand the basic physical processes that take place on different celestial bodies.
Lecturer / Teaching assistant	prof. dr. Mara Šćepanović and prof. dr. Gordana Jovanović
Methodology	Lectures, calculus exercises, colloquiums, seminar papers, consultations, constant testing of knowledge through oral exams and independent study.

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures	A detailed presentation of the plan for the organization of classes and exams, preparation of the first seminar paper. History of astronomy
I week exercises
II week lectures	Test. Cosmological models, Big Bang, microwave background radiation
II week exercises
III week lectures	Test. Electromagnetic radiation of celestial bodies and methods of its measurement,
III week exercises
IV week lectures	Test. Mechanisms and laws of radiation, influence of the Earths atmosphere on astronomical observations.
IV week exercises
V week lectures	Test. Basic astronomical instruments and extraatmospheric astronomy
V week exercises
VI week lectures	Test. Characteristics of stable stars,
VI week exercises
VII week lectures	Test and presentation of the first seminar paper
VII week exercises
VIII week lectures	The structure of the stars
VIII week exercises
IX week lectures	Binary stars and star clusters
IX week exercises
X week lectures	The Milky Way Galaxy
X week exercises
XI week lectures	Star evolution,
XI week exercises
XII week lectures	Changing stars
XII week exercises
XIII week lectures	Extragalactic astronomy
XIII week exercises
XIV week lectures	Sun
XIV week exercises
XV week lectures	Solar system. Presentation of the results and data from the observatory.
XV week exercises

Student workload	per week 6 credits x 40/30=8 hours Structure: 3 hours of lectures, 1 hour of calculation exercises, 4 hours of independent work including consultations/ In the semester Classes and final exam: 8 hours x 16 = 120 hours; Necessary preparations before the beginning of the semester (administration, registration, certification): 2 x 8 hours = 16 hours; Total course load: 6h30=180 hours Additional work on exam preparation in the remedial period, including taking the remedial exam, is from 0 to 44 hours. Load structure: 120 hours (teaching) + 16 hours (preparation) + 44 hours (additional work)
Per week	Per semester
6 credits x 40/30=8 hours and 0 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 0 excercises 5 hour(s) i 0 minuts of independent work, including consultations	Classes and final exam: 8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts Total workload for the subject: 6 x 30=180 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 36 hour(s) i 0 minuts Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations	List the students obligations during classes: Students are required to regularly attend classes, take all tests, write and defend seminar papers.
Consultations	As a rule, after lectures and at the request of students
Literature	Literature: M. Vukićević-Karabin and O. Atanacković: General astrophysics, Dragan Roša and others, Astronomy K. De Pree and A. Akelord: Astronomers, M. Kachelrieß: A Concise Introduction to Astrophysics, B.V. Carroll, D.A. Ostlie: Introduction to Modern Astrophysics, A. R. Choudhuri: Astrophysics for Physicists.
Examination methods	Forms of checking and evaluating knowledge: Six tests with a total of 36 points (up to 6 points for each successfully completed test); One seminar for a total of 14 points (up to 14 points for a successfully completed and defended seminar paper); Presentation of the results and data from the observatory-20 points. Final exam-30 points. A passing grade is obtained if a total of 51 points is collected.
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points

Faculty of Science and Mathematics / PHYSICS / ENVIRONMENTAL PHYSICS

Course:

ENVIRONMENTAL PHYSICS/

Course ID	Course status	Semester	ECTS credits	Lessons (Lessons+Exercises+Laboratory)
10168	Obavezan	6	5	3+1+0

Programs	PHYSICS
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology

Plan and program of work
Preparing week	Preparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises

Student workload
Per week	Per semester
5 credits x 40/30=6 hours and 40 minuts 3 sat(a) theoretical classes 0 sat(a) practical classes 1 excercises 2 hour(s) i 40 minuts of independent work, including consultations	Classes and final exam: 6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts Total workload for the subject: 5 x 30=150 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 30 hour(s) i 0 minuts Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment

Grade:	F	E	D	C	B	A
Number of points	less than 50 points	greater than or equal to 50 points and less than 60 points	greater than or equal to 60 points and less than 70 points	greater than or equal to 70 points and less than 80 points	greater than or equal to 80 points and less than 90 points	greater than or equal to 90 points