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UNIVERSITY OF PÉCS

7622 Pécs Vasvári Pál u. 4. Hungary

Telephone: +36 72 501 500/12418 Fax: +36 72 501 508

E-mail: [email protected]

Centre for International Relations

Physics BSc

Study Abroad Course List for the Fall semester

2018/2019 Faculty of Sciences

Tuition-fee/credit: 100 USD

Course Semester Credits (ECTS)

An insight into Hungary Fall 3

Introductory mathematics p.c. Fall 3

Computer technology I lec. Fall 3

Informatics p.c. Fall 3

Linear algebra lec. Fall 3

Linear algebra p.c. Fall 3

Software packages Fall 3

Introductory mechanics lec. Fall 3

Introductory mechanics p.c. Fall 3

Mathematical methods in physics I p.c. Fall 3

Electricity and magnetism lec. Fall 3

Electricity and magnetism p.c. Fall 3

Modern physics I lec. Fall 3

Electronics lec. Fall 3

Physics and electronics lab. I Fall 4

Electrodynamics lec. Fall 3

Electrodynamics p.c. Fall 3

Electronics p.c. Fall 2

Physics and electronics lab. III Fall 4

Astrophysics lec. Fall 2

Metrology lec. Fall 2

Metrology p.c. Fall 2

Calculus II lec. Fall 2

Calculus II p.c. Fall 3

Discrete mathematics lec. Fall 2

Discrete mathematics p.c. Fall 3

Mathematical methods in physics III p.c. Fall 3

Computer technology II lec. Fall 2

Economics Spring 3

Calculus I lec. Spring 3

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Calculus I p.c. Spring 3

Mathematical methods in physics II p.c. Spring 3

Thermodynamics lec. Spring 3

Thermodynamics p.c. Spring 3

Waves and optics lec. Spring 3

Waves and optics p.c. Spring 3

Modern physics II lec. Spring 3

Classical mechanics lec. Spring 3

Classical mechanics p.c. Spring 3

LabVIEW basics p.c. Spring 3

Physics and electronics lab. II Spring 4

Lasers and their applications lec. Spring 2

Numerical methods lec. Spring 2

Numerical methods p.c. Spring 3

Computer programming I p.c. Spring 3

Computer programming II p.c. Spring 3

Quantum mechanics lec. Spring 3

Quantum mechanics p.c. Spring 3

Detailed information about the courses:

Course title: An insight into Hungary

Language of instruction: English

Teaching period: Fall Semester

Class hours per week: 2

Credits (ECTS): 3

Course objectives: The main objective is to provide an overview ont he country (Hungary)

and place (Pécs), where the targeted international students continuing their cross cultural

studies. The civilisation course intends to introduce some important and characteristic aspects

of our heritage, culture and also the social profile of Hungary.

Course description: 1. A brief history of Hungary - turbulent centuries at the crossroads of Europe

2. Characteristic features of state socialism as an important era of our recent past

3. Transition period - orientation changes

4. The country as a full member of EU

5. Physical resources of Hungary

6. Hungary: facts and figures

7. Social-demographic profile of Hungary

8. Economic issues of Hungary

9. Settlement pattern of Hungary

10. Pécs within the spatial structure of Hungary

11. Political system of Hungary of Europe in 2010

Assessment methods: Written final test

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Introductory mathematics p.c.


Teaching period: Fall Semester


Credits (ECTS): 3

Course objectives: Acquiring the basic mathematical skills essential for higher level

mathematics and physics courses.

Course description:

Solving equations

1. First and second degree equations, linear systems of equations.

2. Trigonometric, logarithmic, exponential equations.

Fundamentals of algebra

1. Properties of exponentiation. Basic algebraic identities. The binomial theorem.

2. Roots of polynomials, factoring polynomials. Division among polynomials.

3. Operations with rational functions.

Basic functions

1. Plotting functions. Function examination.

2. Linear functions, power functions, polynomial functions.

3. Trigonometric and inverse trigonometric functions.

4. Exponential and logarithmic functions. Hyperbolic functions.

Assessment methods: Weekly assignments and two midterm tests.

Course title: Computer technology I lec.


Teaching period: Fall


Credits (ECTS): 3

Course objectives: The course discusses the substantial knowledge for computer technology.

Serves as a foundation of further, more advanced subjects

Course description: Boolean algebra and binary arithmetic, number representations,

Transformation and simplification of boolean functions. Canonical forms of boolean

functions, systematic simplification methods. Hazards and their elimination. Sequential

circuits, storage components. Design of sequential circuits, synchronous and asynchronous

circuits. Microprogrammed sequential circuits.

Assessment methods: Oral exam

Course title: Informatics p.c.




Credits (ECTS): 3

Course objectives: knowledge of the standard rules of the document creation, the knowledge

of the standard formats of presentations. The capability to obtain information on the internet.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course description: 1. Introduction. Standard knowledge of informatics. Rules of document creation.

2. Rules of document creation. Letter, Rules of CVs.

3. Thesis, report. Header, footer, styles and automatic table of contents.

4. Thesis, report. Equation editor, list of figures, embedded spreadsheets.

5. Exam 1: word processing

6. Introduction to spreadsheets. Absolute and relative references, cell formatting.

7. Spreadsheets. Embedded functions, data representation

8. Spreadsheets. Report creation.

9. Exam 2: Report (word processing, spreadsheets).

10. Presentation. Rules and possibilities of creating presentations.

11. Presentation, LaTeX. Student presentations and introduction to LaTeX

12. Internet. Search engines (Google, Yahoo, Bing), problem solving via the internet

(Wolfram Alpha).

13. Scientific resources: Web of Science, Science Direct, arXiv

Assessment methods: 2 written exams and homework assignments

Course title: Linear algebra lec.




Credits (ECTS): 3

Course objectives: Compulsory course for BSc students in Physics, covers the basic

algebraic methods used in Physics. Lays the ground for further subjects, like quantum

physics, matrix optics, etc.

Course description: Linear equation systems and their solution with elimination, matrices

and operations on them, adding, multiplying with numbers, multiplying and transposing.

Partitioned matrices and the properties of their operations. Augmented matrices of linear

systems.Solution of linear equation systems, inverting matrices, nonsingular matrices.

Reduced row echelon form of matrices and basic operations on them, row and column

equivalency. Gauss elimination, Gauss-Jordan reduction. Solution of linear equation system.

The calculation of inverse matrices. Special matrices. Equivalent matrices. The determinant

and its properties. Determining determinants with subdeterminants. Determining matrix

inverses with determinants. Real vector spaces, the isomorphism of real vector spaces. Rn as

vector space. Coordinates.Linear combination, subspaces of a real vector space. Linear

independence, dimension, basis. Properties of the solution of linear equations. Rank and

nullityof matrix, relation to linear equation systems. Normed spaces, spaces with inner

products. CauchySchwarz inequality. Cross product of vectors in three dimensions, properties

of operations, the Levi-Civita symbol and it’s application. Orthogonality, orthonormed basis,

Gram-Schmidt orthogolalization. Orthogonal complementers and it’s properties. Nullspace,

row, clumnspace of matrix and their relation. Linear operators and operations on them.

Nullspace (kernel) and image. Matrices of linear operators as general and on orthonormed

basis. Operators in matrix representation. Changing the basis in general and between

orthonormed basis. Similarity of matrices. Eigenvalue and vector, determining them. The

multiplicity of eigen values eigensubspaces. Similarity and diagonalisability. Spectral

decomposition of symmetric matrices.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Assessment methods: Exam

Course title: Linear algebra p.c.




Credits (ECTS): 3

Course objectives: Compulsory course for BSc students in Physics, covers the basic

algebraic methods used in Physics. Lays the ground for further subjects, like quantum

physics, matrix optics, etc

Course description: Linear equation systems and their solution with elimination, matrices

and operations on them, adding, multiplying with numbers, multiplying and transposing.

Partitioned matrices and their operations. Augmented matrices of linear systems. Solution of

linear equation systems, inverting matrices, nonsingular matrices. Reduced row echelon form

of matrices and operations on them, row and column equivalency. Gauss elimination, Gauss-

Jordan reduction. Solution of linear equation system. The calculation of inverse matrices.

Determining determinants with subdeterminants. Determining matrix inverses with

determinants. Coordinates. Linear combination, subspaces of a real vector space. Linear

independence, dimension, basis. Properties of the solution of linear equations. Inner products.

Cross product of vectors in three dimensions, the Levi-Civita symbol and it’s application.

Nullspace, row, columnspace of matrix and their relation. Linear operators and operations on

them. Nullspace (kernel) and image. Matrices of linear operators as general and on

orthonormed basis. Operators in matrix representation. Changing the basis in general and

between orthonormed basis. Eigenvalue and vector, determining them. Similarity and

diagonalisability. Spectral decomposition of symmetric matrices.

Assessment methods: Test

Course title: Software packages




Credits (ECTS): 3

Course objectives: Introduction into the program packages, most frequently used in

modeling physical problems and data processing.

Course description:

Data processing and mathematical software packages: Origin, Gnuplot, Maple,

Matlab/Octave

1. Origin: the Origin workspace; worksheets, data import, and plotting; working with

Excel in Origin; data exploring; creating multiple layer graphs; 3D surface and

contour graphs; nonlinear curve fitting; creating presentations with the layout page.

Developing specialized problems in Origin.

2. Gnuplot: basics; command-line input and scripts; plotting; invoking system

commands; curve fitting; loading script files; graph parameters; determining output

terminal; 3D graphs. Developing specialized problems in Gnuplot.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


3. Maple: Numerical calculations: using Maple as a calculator; algebraic expressions

and formulae; solving equations, approximate solutions; functions: definition,

substitution, graph; procedures: local and global variables; matrices, matrix

arithmetics, Gaussian elimination, eigenvalues and eigenvectors

4. Matlab/Octave: variables (scalar, vector, matrix), assignment; mathematical

expressions; graphical presentation: 2D and 3D plots; programming: scripts, functions,

loops, conditional statements

Assessment methods:

Average of homeworks 25 %

Average of 2 written exams 75 %

The course cannot be completed if any of the two written examinations is marked as

unsatisfactory.

Course title: Introductory mechanics lec.




Credits (ECTS): 3

Course objectives: Mastering the basic mechanical concepts, and acquiring general skills in

scientific reasoning through the subject of mechanics.

Course description:

1. The kinematics of material point. Uniform motions. Motion with constant

acceleration. Free fall, projectile motions. The circular motion. The simple harmonic

motion.

2. Dynamics of material point: Different type of forces. Free motion. Contact motions.

Dynamics of systems of points.

3. Determination of different type of works. Work-energy theorem. The potential and

kinetic energy. The conservation of energy. Momentum and angular momentum of a

system. Collisions.

4. Equilibrium of rigid bodies. Kinematics of rigid bodies. Dynamics and energy of rigid

bodies.

5. The gravitational field: field strength and potential. The planetary motion. Kepler’s

laws.

6. The inertial forces.

7. Mechanics of elastic bodies: the state of deformation.

8. Flow of ideal and viscous fluids.

9. The harmonic oscillator. Small oscillations. Addition of harmonic oscillators. The

damped oscillator. The driven oscillator. Propagation, reflection and refraction of

waves. Interference, standing waves. Diffraction.

10. The Doppler-effect.


UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Introductory mechanics p.c.




Credits (ECTS): 3

Course objectives: Mastering the basic mechanical concepts, and acquiring general skills in

scientific reasoning through the subject of mechanics.

Assessment methods: Written examination in semester: 50%, oral examination: 50%

Course title: Mathematical methods in physics I p.c.




Credits (ECTS): 3

Course objectives: The course focuses on basic mathematical skills required for studying

physics, but usually acquired by the students only much later in mathematics courses. New

material is always presented first in an intuitive way without rigorous mathematical proofs

and then the emphasis is on independent problem solving.

Course description:

1. Differentiation of real functions of a single variable.

2. Definite and indefinite integrals of real functions of a single variable.

3. Applications of definite integrals.

4. Complex numbers and functions of a complex variable.

5. Vectors, bases, linear transformations and their matrix representation.

Assessment methods: Midterm and Final test

Course title: Electricity and magnetism lec.




Credits (ECTS): 3

Course objectives: Developing knowledge and understanding of the concepts of electricity

and magnetism.

Course description:

Electrostatics

1. Electric field in vacuum, Coulomb’s law, Elementary charge and the most important

special distributions of it, Work of the electric field, work and electric potential,

determination of the elementary charge, electric capacitance, capacitors, electrostatic

devices, Energy of the electric field, dielectrics, The electric polarization and field

strength in dielectrics, The fundamental electrostatic laws in dielectrics

The laws of direct currents

2. Ohm’s law, Various forms of Ohm’s law, Kirchhoff’s laws, Resistances in series and

parallel, current and volt-age measurement devices, measuring resistances, Serial and

parallel battery configurations, Electric work and power of direct current

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Magnetostatics

3. Basic magnetic phenomena, magnetic field, flux of the magnetic field, forces in

magnetic field, Biotlaw, Earth magnetism, Magnetic induction and field strength,

magnetic properties of solids, magnetic circuits

Current conduction phenomena

4. Free electrons in metals, band theory of metals, Electron energy distribution in

conductors, Thermionic electron emission and work function, contact potential,

thermoelectric effects, semiconductors, different types of semiconductors, current in

dielectrics, electrolytic dissociation and electrolysis, batteries, charge transport in

vacuum, electron microscope, electron tubes, electric conduction in gases, gas

discharges, natural electrostatic discharges

Electromagnetic induction

5. Faraday induction, mutual induction, energy of the magnetic field, transient signals in

dc circuits, electromagnetic oscillations, Impedance, forced oscillations in serial and

parallel RLC circuits, Electric work and power of alternating currents, free

electromagnetic oscillations in closed RLC circuits, coupled electromagnetic

oscillations, measuring inductance and capacitance, high frequency oscillations


Course title: Electricity and magnetism p.c.




Credits (ECTS): 3

Course objectives: Developing knowledge and understanding of the concepts of electricity

and magnetism. Getting experience in calculations with electric and magnetic fields, currents,

charges.

Course description: 1) The Coulomb force. Interaction between electrical charges.

2) The electrical field strength and potential.

3) Mass of charges, equipotential surfaces, Gauss-law, mirror charges.

4) Capacitors. The connection of capacitors. Dielectrics.

5) The direct current, Ohm's law.

6) Connection of electrical sources.

7) DC circuits, Kirchhoff’s rules.

8) Magnetostatics. Lorentz force.

9) Induction by direct current. The Biot-Savart law.

10) Conducting lines, current loops, solenoids, toroids.

11) Magnetic materials. Magnetic resistance.

12) The electromagnetic induction.

13) The alternating current (AC). The effective value.

14) Simple unsteady circles.

15) Resistance in AC. The RLC circuit.

16) Resonant-frequency and radiation in oscillating circuits.

17) AC circuits.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Assessment methods: Discussion credit. The students have to write 2 essays, and 2 marks are

given to them. The credit mark will be the average of the 2 marks (rounded up), if the marks

greater than 1. Students could improve their credit mark by 1 by regular homework doing.

Course title: Modern physics I lec.




Credits (ECTS): 3

Course objectives: Introduction into principal knowledge of modern physics, basics of

quantum mechanics, atomic, nuclear and solid state physics, scientific and technologic

applications, basics of modern cosmology

Course description:

1) Waves. Interference. Diffraction. Standing waves. Fourier transformation. Wave

packets.

2) Atoms. The structure of atoms.

3) Quantized nature of light: Blackbody radiation. Photoelectic effect. Compton-

scattering.

4) Matter waves. Elektronmicroscope. Neutrondiffraction.

5) Bohr-modell.

6) Basic quantum mechanics. –

7) Wave function and its interpretation. Schrödinger-equation.

8) Potential well. Harmonic oscillator. Transmission through a potential barrier; scanning

tunneling microscope.

9) The Hidrogen atom.

10) The electron spint. Spin in magnetic field.

11) Periodic table. Electronic structure of atoms. Pauli exclusion principle.

12) Chemical bonds.

13) Molecule. Rotation and vibration of molecules.

14) Absorpcion and emission of light. Optical and x-ray spectra.

15) Test.


Course title: Electronics lec.




Credits (ECTS): 3

Course objectives: Principle of the electronic and electronic measurements theory and use, to

acquire knowledge about simple circuits and components, electronic systems, measure-

control and the principle of digital data processing

Course description: 1) Subject of electronics; passive and active networks - characteristics and use (R, L, C

components, generators)

2) Passive networks, filters, properties of networks time-range and frequency

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


3) Nonlinear bipolar networks, property of diodes (signal processing circuits with diodes

and rectifier circuits)

4) Principle of transistors, characteristics and use of amplifier circuits Feedback in

amplifier, oscillators Principle of Operation amplifier, characteristics and use

5) Signal-processor circuits, multivibrators

6) Logical circuits, combination logics network

7) Sequence networks: electronic latch, counters

8) A/D, D/A converters, measure-control

9) Digital data processing, microcontrollers

10) Control-circuits, electronic sensors


Course title: Physics and electronics lab I.




Credits (ECTS): 4

Course objectives: Acquiring experimental skills, interpretation of measurement data, proper

documentation of measurements.

Course description: 1) Methods of measuring mass. Mass measurement by means of uniform rotary motion

and harmonic oscillation.

2) Measuring of spring constant.

3) Measuring of free fall acceleration with falling ball and by means of a simple

pendulum.

4) Determination of inertial moment by means of uniformly accelerating rotation. Inertial

moments of cylinders of equal mass.

5) Surface-tension of liquid. Measurement by means of ring method and drop count

method. Absolute and relative method.

6) Density and viscosity of liquid. Mohr-Westphal balance and the relative measurement.

Falling ball viscometer.

7) Measuring of frequency and time period by means of stroboscope and tachometer.

8) Measuring refractive index and partial dispersion of liquid. Abbe refractometer.

Determination of refractive index of glass prism by means of a goniometer.

9) Optical activity. Specific opticalrotatory power of sugar solution. Reflection of

polarized light. Fresnel’s equations.

10) Determination of extent of miniature by microscope and diffraction of light. Slit, hole,

grating, CD.

11) Determination of focal length of thin lens. Study of lens aberrations. Spherical and

chromatic aberration.

12) The distribution of laser light.

13) Study of polarized light. Malus’ law. Optical fiber and polarization

Assessment methods: Students have to report for evaluation of laboratory exercises in lab

book.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Electrodynamics lec.




Credits (ECTS): 3

Course objectives: Required course of Physics BSc studies. Its aim is to improve analytical

and problem solving skills by placing treatment of electrodynamics’ phenomena on a more

general foundation.


Course title: Electrodynamics p.c.




Credits (ECTS): 3

Course description:

1) Electric charge and electric field, basic equations of electrostatics. Poincaré identities,

the electrostatic potential.

2) Poisson equation and its solution. Gauss and Stokes theorem. Dipole moment and

polarization, electrostatics of dielectrics, metals.

3) Magnetic field, Lorentz force, vector potential. Magnetostatics of polarizable media.

4) Law of induction, charge conservation and displacement current. Maxwell’s equations

in vacuum and medium.

5) Wave equation and its plane wave solution. Dispersion, field energy, field momentum.

Refraction and reflection of monochromatic plane wave on the boundary of two

dielectrics.

6) Galilean and Einstein relativity. Lorentz transformation, time dilation, length

contraction. Proper time, the twin paradox

Assessment methods: Written exam

Course title: Physics and electronics lab. III




Credits (ECTS): 4

Course objectives: : Acquiring experimental skills, interpretation of measurement data,

proper documentation of measurements


book.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Astrophysics lec.




Credits (ECTS): 2

Course objectives: The course gives an overall introduction into astrophysics. It uses the

preliminary knowledge of students in a wide range of physics fields, and provides an example

for the application of those. The objective of the subject is to give strong basis for

understanding the main concepts and the importance of new scientific achievements in

astronomy.

Course description: 1) Main parts of astronomy, its connections with other sciences –

2) Instrumentation /1. (collecting and transforming the incoming radiations: telescopes;

their history) –

3) Instrumentation /2. (sensing the radiations: detectors), methods of radiation studies

(photometry, spectroscopy, -

4) Stellar astrophysics /1. (physical parameters of the stars, and theirs measurements;

their values) –

5) Stellar astrophysics /2. (correlations between certain physical parameters; MLR and

HRD; classification) –

6) Stellar astrophysics /3. (description of the Stellar interiors; equilibrium stellar models)

- Nearest star: the Sun (resolved surface and atmosphere; wide variety of events;

activity; problems) –

7) Stellar astrophysics /4. (modeling & basics of the stellar evolution; evolutionary

scenarios contra initial masses; evolutionary tracks on HRD) –

8) Stellar astrophysics /5. (variable stars, binary stars, binary evolution) –

9) Interstellar material (appearance, observability, types and main properties of

interstellar clouds) –

10) The Milky Way (history, stellar populations, distributions of its different constituents,

dynamics, spiral arms, long-term evolutionary considerations; dark material and its

discovery)

11) Extragalactic astronomy (Local Group galaxy system; morphology of extragalaxies,

main properties, largescale distribution of galaxies: clusters and empty spaces) –

12) The Universe (Big Bang theory, overview on its evolution, most important phases,

observational cosmology: the observable evidences of the Big Bang: CBR,

cosmological redshift)

Assessment methods: written examination (test)

Course title: Metrology lec.




Credits (ECTS): 2

Course objectives: Introduction into the basic principles of measuring physical and other

quantities and into the statistical interpretation of measurement data.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course description:

1) Measurements in physics (modelling, verification, validation, measurement, basic and

derived units)

2) Units, etalon, measuring instruments, measurement instructions, analogue and digital

devices

3) Basic units of SI and their measurement

4) Measurement of on-electric signals

5) Calibration of the acquisition system, validation of measured data

6) Uncertainty of the measured data, systematic and random errors, propagation of errors.

7) Basic measurement statistics (normal distribution, expected value, standard deviation,

confidence interval, statistical probes))

8) Digital data acquisition, sampling theorem

9) Fourier analysis

10) Correlation analysis

11) Interpretation of data (curve fitting, regression, linearization)


Course title: Metrology p.c.




Credits (ECTS): 2

Course objectives: Introduction into the basic statistical interpretation of measurement data.

Course description: 1) Practical problem solving on the basis of the lecture topics

2) Basic units of SI and their measurement

3) Measurement of on-electric signals

4) Calibration of the acquisition system, validation of measured data

5) Uncertainty of the measured data, systematic and random errors, propagation of errors.

6) Basic measurement statistics (normal distribution, expected value, standard deviation,

confidence interval, statistical probes))

7) Digital data acquisition, sampling theorem

8) Fourier analysis

9) Correlation analysis

10) Interpretation of data (curve fitting, regression, linearization)


Course title: Calculus II lec.




Credits (ECTS): 2

Course objectives: The students learn about the basics of mathematical analysis, which is

required for the deeper understanding of physical phenomena.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course description: Integration - The definite integral. Indefinite integrals, the Fundamental Theorem of Calculus.

- Integration using substitution. Integration by parts. - Integration of rational functions by

partial fractions. - Trigonometric and hyperbolic integrals. Trigonometric and hyperbolic

substitutions. - Improper integrals. - Numerical integration. Applications of definite integrals -

Calculating areas and volumes. Lengths of plane curves. Solids and surfaces of revolution. -

Moments, centers of mass, work, fluid pressures and forces. First order ordinary differential

equations - Slope fields, separable differential equations. First order linear differential

equations. - Numerical solution of differential equations. Autonomous differential equations.

Infinite series - Convergence tests. - Power series, applications of power series. Fourier series.

Vector-valued functions - Vector-valued functions and their differentiation. Arc length along

a space curve. Differential calculus of functions of several variables - Limits and continuity in

higher dimensions. - Partial derivatives. The Chain Rule. Taylor's formula in higher

dimensions. - Directional derivatives, gradient vectors. - Finding extreme values. - Partial

derivatives with constrained variables. Multiple integrals - Double and triple integrals. Area,

volume, moments and centers of mass. - Double integrals in polar form. Triple integrals in

cylindrical and spherical coordinates. - Substitutions in multiple integrals.


Course title: Calculus II p.c.




Credits (ECTS): 3


required for the deeper understanding of physical phenomena

Course description: 1) Integration

- The definite integral. Indefinite integrals, the Fundamental Theorem of

Calculus.

- Integration using substitution. Integration by parts.

- Integration of rational functions by partial fractions.

- Trigonometric and hyperbolic integrals. Trigonometric and hyperbolic

substitutions.

- Improper integrals.

- Numerical integration.

2) Applications of definite integrals

- Calculating areas and volumes. Lengths of plane curves. Solids and surfaces of

revolution.

- Moments, centers of mass, work, fluid pressures and forces.

3) First order ordinary differential equations

- Slope fields, separable differential equations. First order linear differential

equations.

- Numerical solution of differential equations. Autonomous differential

equations.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


4) Infinite series

- Convergence tests.

- Power series, applications of power series. Fourier series.

5) Vector-valued functions

- Vector-valued functions and their differentiation. Arc length along a space

curve.

6) Differential calculus of functions of several variables

- Limits and continuity in higher dimensions.

- Partial derivatives. The Chain Rule. Taylor's formula in higher dimensions.

- Directional derivatives, gradient vectors.

- Finding extreme values.

- Partial derivatives with constrained variables.

7) Multiple integrals

- Double and triple integrals. Area, volume, moments and centers of mass.

- Double integrals in polar form. Triple integrals in cylindrical and spherical

coordinates.

- Substitutions in multiple integrals.

Assessment methods: Midterm and final test

Course title: Discrete mathematics lec.




Credits (ECTS): 2

Course objectives: To introduce basic mathematical and discrete mathematical notions and

ideas

Course description: Basic concepts of set theory, operations with sets. Relations, inverse

relations, equivalence, partial ordering, total ordering, classes. Relation between equivalence

relation and class partition. Function as a relation, types of functions, operations, product of

relations. Associativity of product of relations. Basic concepts of combinatorics,

permutations, variations, combinations (with repetition, too). Binomial theorem, polynomial

theorem, identities about binomial coefficients, inclusion-exclusion formula. Recursion,

Fibonacci and Catalan numbers. Construction of the idea of numbers. Natural numbers,

Peano's axioms. Basic concept of graph theory, graph isomorphism, paths, cycles,

connectivity, tree, spanning tree. Number of cycles in a graph, cut, number of cuts, Kruskal's

algorithm, planar graphs, Euler's formula, Kuratowski's graphs. Euler and Hamilton cycles.

Directed graph, strongly connected components. Graphs and matrices.

Assessment methods: Final exam

Course title: Discrete mathematics p.c.




Credits (ECTS): 3

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course objectives: To introduce basic mathematical and discrete mathematical notions and

ideas.

Course description: Problems and exercises related to the following topics: Basic concepts

of set theory, operations with sets. Relations, inverse relations, equivalence, partial ordering,

total ordering, classes. Relation between equivalence relation and class partition. Function as

a relation, types of functions, operations, product of relations. Associativity of product of

relations. Basic concepts of combinatorics, permutations, variations, combinations (with

repetition, too). Binomial theorem, polynomial theorem, identities about binomial

coefficients, inclusion-exclusion formula. Recursion, Fibonacci and Catalan numbers.

Construction of the idea of numbers. Natural numbers, Peano's axioms. Basic concept of

graph theory, graph isomorphism, paths, cycles, connectivity, tree, spanning tree. Number of

cycles in a graph, cut, number of cuts, Kruskal's algorithm, planar graphs, Euler's formula,

Kuratowski's graphs. Euler and Hamilton cycles. Directed graph, strongly connected

components. Graphs and matrices.

Assessment methods: 2 Midterm exams

Course title: Mathematical methods in physics III p.c.




Credits (ECTS): 3

Course objectives: The course focuses on basic mathematical skills required for studying

physics, but usually acquired by the students only much later in mathematics courses. New

material is always presented first in an intuitive way without rigorous mathematical proofs

and then the emphasis is on independent problem solving.

Course description:

Differential equations

1) Notion and classification of differential equations, classification of solutions

2) Obtaining differential equations, initial value problems

3) First order differential equations, separable differential equations, equations reducible

to separable differential

4) equations, exact differential equations

5) Linear first order differential equations, differential equations reducible to linear

differential equations

6) Second order differential equations, linear differential equations, incomplete

differential equations

Probability theory

7) Basic combinatorics

8) Events, notion of classical probability, axioms of probability theory

9) Conditional probability, Law of total probability, Bayes’ theorem, independent events

10) Random variables, cumulative distribution functions, expectation value, variance,

moments

11) Most important discrete probability distributions

12) Continuous probability distributions and their moments, distribution of transformed

random variables

13) Most important continuous probability distributions

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Assessment methods: Midterm and Final test

Course title: Computer technology II lec.




Credits (ECTS): 2

Course objectives: The course discusses the basic computer hardware and their architecture,

in the perspective of the evolution of the technology.

Course description: Three bus architecture of computers, bus systems. Structure and

operation of memory elements: dynamic and static memory, RAM, ROM, PROM, EPROM,

EEPROM. The inner structure of processors, operation and services. Memory addressing,

memory protection, privilege levels, task handling, I/O handling, interrupt system,

multiprocessor systems.

Computer peripherals: structure and principles of operation. Storage solutions. Magnetic,

optical and magnetooptical media. Floppy drive, Hard disk drive, CD-ROM. Magnetic tape

storage solutions. Type of printers, modes of operation. Digitizing tablets, scanners and

graphic pointers.


Course title: Economics


Teaching period: Spring


Credits (ECTS): 3

Course objectives: The course is designed to help students understand the basics of

economic principles. It teaches them how economics relates to the everyday life of individuals

or business. After the course, students should have a better understanding of everyday

economic issues.

Course description:

1) Economics basics (definitions, production possibility frontier, the circular flow, types

of resources)

2) History of economic thought I.

3) History of economic thought II.

4) Basics of macroeconomics

5) Economic basics: supply and demand

6) Economic basics: monopolies, oligopolies and perfect competition

7) Economic policy: fiscal and monetary policy. Tools and goals

8) Unemployment (definition, measures, effects, types of unemployment and causes)

9) Inflation (History, definition, measures, effects, causes, controlling)

10) History of the money: from barter to banknotes and electronic money

11) The banking systems (history, types of the banks, activities, banks in the economy)

12) Basics of international economics


UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Calculus I lec.




Credits (ECTS): 3


required for the deeper understanding of physical phenomena..

Course description:

1. Preliminaries

a. Basics of set theory. Natural numbers, integers and rational numbers.

Algebraic, order and completeness properties of the real line. Decimal

representation of real numbers. Absolute value and its properties, intervals.

b. The notion of functions. Domain, range and graph of functions. Ways to define

functions. Basic function types. Sum, difference, product and quotient of

functions. Composite functions. Transformations of graphs of functions.

2. Limits and continuity

a. Average and instantaneous rates of change. Calculating limits.

b. The precise definition of a limit. Theorems concerning limits. One-sided

limits.

c. Limits at infinity. Infinite limits. Horizontal, oblique and vertical asymptotes.

d. Continuity. Operations with continuous functions. Compositions of continuous

functions. Continuous extensions of functions. The Intermediate Value

Theorem for Continuous Functions.

3. Differentiation and its applications

a. Tangent to a curve. Derivative at a point.

b. Derivative functions. Relation between differentiability and continuity.

c. Derivatives of powers, sums, products and quotients. Derivatives of

trigonometric functions. Higher order derivatives.

d. The derivative as a rate of change. Motion along a line: displacement, velocity,

acceleration. Derivatives in economics.

e. Derivatives of inverse functions. The Chain Rule. - Parametric curves, slopes

of parametrized curves. Implicitly defined functions, implicit differentiation.

Related rates. Linearizations.

f. Local and global extrema. Extreme values of continuous functions. Finding

exterma.

g. Rolle's Theorem. The Mean Value Theorem and its consequences.

h. Connection between monotonity of a function and its first derivative.

Concavity and points of inflection. Graphing functions using their first and

second derivatives.

i. Applied optimization problems.

j. Cauchy's Mean Value Theorem. L'Hospital's Rule.

k. Finding roots using Newton's method.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


4. Infinite sequences and series

a. Infinite sequences. Limits of convergent sequences. Divergent sequences.

Calculating limits of sequences.

b. Monotonic and bounded sequences. Commonly occuring limits.

c. Infinite series. Convergent and divergent series. Operations with series,

reindexing series. Basic convergence test. Absolutely convergent series.


Course title: Calculus I p.c.




Credits (ECTS): 3

Course objectives: The students solve problems concerning the basics of mathematical

analysis, developing logical reasoning, analysis, problem-solving skills, creativity, abstract

thinking, and the ability to use apply the learnt methods in solving physics problems.


Course title: Mathematical methods in physics II p.c.




Credits (ECTS): 3

Course objectives: Acquire knowledge and computation skill in vector analysis that is

necessary for the courses on Theoretical Mechanics and on Electrodynamics in particular.

Course description:

1. Scalar fields, niveau surfaces, directional derivatives, the gradient.

2. Vector fields, line integral, Poincaré’s 1st Lemma and Stokes’ Theorem.

3. The flux and divergence of vector fields. Gauss’ Theorem. Poincaré’s 2nd Lemma

4. Matrix representation of linear transformations.

5. The index notation: usage of Kronecker and Levi-Civita symbols.

6. All of these illustrated by a bunch of exercises and problems.


Course title: Thermodynamics lec.




Credits (ECTS): 3

Course objectives: Mastering the basic thermodynamic concepts, and acquiring general skills

in scientific reasoning through the subject of thermodynamics


UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Thermodynamics p.c.




Credits (ECTS): 3

Course objectives: Mastering the basic thermodynamic concepts, and acquiring general skills

in scientific reasoning through the subject of thermodynamics

Course description: 1. Empirical temperature, state-equation

2. The molecular structure of material

3. The major principles of thermodynamics, and their applications

4. The entropy

5. Phase transitions


Course title: Waves and optics lec.




Credits (ECTS): 3

Course objectives: The major learning outcomes for this course are Problem Solving and

Quantitative Reasoning. Upon successful completion of the course, the student must be able

to understand the basic concepts of oscillations, waves and optics. Students will have the

basic understanding of both geometrical and wave optics. They will be able to solve simple

problems by studying the appropriate equations describing optical and general wave

phenomena.

Course description:

Oscillations.

Harmonic and anharmonic oscillations. Differential equation of harmonic motions.

Mathematical

pendulum, anharmonicity. Result of more harmonic motions, beating. Decomposition of

oscillations. Fourierseries.

Damped oscillations, forced oscillations, their differential equations. Resonance. Coupled

oscillation.

Waves.

Types of waves, polarization. Wavelength, traveling velocity. Function of a wave traveling

along a line.

Traveling velocity of longitudinal and transversal mechanical waves. One dimensional wave-

equation and its

solutions. The principle of superposition. Interference of waves, constructive and destructive.

Standing wave,

resonant frequency. Wave-group. Phase- and group velocity. Reflection, refraction and

interference of twodimensional

waves. Huygens and Huygens-Fresnel principle. Wave-function of three dimensional waves.

Plane-wave, spherical wave. Energy density in wave.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Sound.

Production and sensing of sound. Properties of sound. Measuring of sound intensity, the

decibel scale.

Sensing of sound, the unit of phone. Measurement of the speed of sound. Doppler effect.

Head-wave, Machnumber.

Geometrical optics.

Propagation of light. Velocity of light. Reflection and refraction. Total reflection. Plane

and spherical mirrors. Lenses and thick lenses. Lens systems. Aberration of lens. Camera,

projectors. Magnifier,

microscopes, telescopes. Eye. Colors.

Wave optics.

Wave theory of light. Superposition and dispersion. Coherence condition and interference.

Interferometers.

Dielectric layers. Diffraction. Gratings. Atmospheric light phenomena. Holography.

Polarization.

Birefringence. Optical activity. Photometry. Absorption.

Assessment methods: Oral exam. Maximum number of absence is: 3.

Course title: Waves and optics p.c.




Credits (ECTS): 3

Course objectives: The major learning outcomes for this course are Problem Solving and

Quantitative Reasoning. Upon successful completion of the course, the student must be able

to understand the basic concepts of oscillations, waves and optics. Students will have the

basic understanding of both geometrical and wave optics. They will be able to solve simple

problems by studying the appropriate equations describing optical and general wave

phenomena.

Course description:

Oscillations.

Harmonic and anharmonic oscillations. Differential equation of harmonic motions.

Mathematical

pendulum, anharmonicity. Result of more harmonic motions, beating. Decomposition of

oscillations. Fourierseries.

Damped oscillations, forced oscillations, their differential equations. Resonance. Coupled

oscillation.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Waves.

Types of waves, polarization. Wavelength, traveling velocity. Function of a wave traveling

along a line.

Traveling velocity of longitudinal and transversal mechanical waves. One dimensional wave-

equation and its

solutions. The principle of superposition. Interference of waves, constructive and destructive.

Standing wave,

resonant frequency. Wave-group. Phase- and group velocity. Reflection, refraction and

interference of twodimensional

waves. Huygens and Huygens-Fresnel principle. Wave-function of three dimensional waves.

Plane-wave, spherical wave. Energy density in wave.

Sound.

Production and sensing of sound. Properties of sound. Measuring of sound intensity, the

decibel scale.

Sensing of sound, the unit of phone. Measurement of the speed of sound. Doppler effect.

Head-wave, Machnumber.

Geometrical optics.

Propagation of light. Velocity of light. Reflection and refraction. Total reflection. Plane

and spherical mirrors. Lenses and thick lenses. Lens systems. Aberration of lens. Camera,

projectors. Magnifier,

microscopes, telescopes. Eye. Colors.

Wave optics.

Wave theory of light. Superposition and dispersion. Coherence condition and interference.

Interferometers.

Dielectric layers. Diffraction. Gratings. Atmospheric light phenomena. Holography.

Polarization.

Birefringence. Optical activity. Photometry. Absorption.

Assessment methods: Maximum number of absence is: 3.

Homeworks 33%, + 2 Midterm exams 66%

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Modern physics II lec.




Credits (ECTS): 3

Course objectives: Principles of modern physics: quantum mechanics, atomic physics,

nuclear physics, solid-state physics; scientific and technical applications

Course description: Atomic nucleus. Structure and size. Mass and binding energy. Forces.

Radioactive decay and nuclear reactions. Beta, gamma, and alpha decay. Fission and fusion.

Elementary particles. Hadrons and leptons. Conservation laws. Quarks. Force carrier

particles. Particle accelerators and detectors.

Condensed matters. Structure description of crystalline materials. Crystal lattice.

Crystal diffraction and reciprocal lattice.

Lattice vibrations. Phonons. Infrared absorption. Raman scattering. Inelastic scattering of

neutrons.

The phonon contribution to the specific heat. Interaction between thermal conduction and

phonons.

Free electron Fermi gas. Specific heat of electron gas.

Band structure of solids. Dopant energy levels.

Electric, optical and magnetic properties of solids. Superconductivity.

Micro- and nanostructures. Liquids and polymers.

Microscopy techniques for materials science.

Test.

Assessment methods: Test

Course title: Classical mechanics lec.




Credits (ECTS): 3

Course description: Introduction: basic notions of mechanics. Newton's laws for point

particles. Dynamics of a particle, energy, momentum, angular momentum. Systems with one

degree of freedom. Equilibrium and its stability, small oscillations (damped and driven

harmonic oscillator). Dynamics of a system of point particles; energy, momentum, angular

momentum. Constraints, the Lagrangian formulation of mechanics. The principle of least

action. Generalized momenta, symmetries and conservation laws. The gravitational two-body

problem, Kepler's laws. Non-inertial (accelerating and rotating) frames of reference. Rigid

bodies (kinematics, dynamics, the inertia tensor). Rotation around a fixed axis, planar motion

of rigid bodies. Torque-free motion of the spherical and symmetric top.


UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Classical mechanics p.c.




Credits (ECTS): 3

Course description: Introduction: basic notions of mechanics. Newton's laws for point

particles. Dynamics of a particle, energy, momentum, angular momentum. Systems with one

degree of freedom. Equilibrium and its stability, small oscillations (damped and driven

harmonic oscillator). Dynamics of a system of point particles; energy, momentum, angular

momentum. Constraints, the Lagrangian formulation of mechanics. The principle of least

action. Generalized momenta, symmetries and conservation laws. The gravitational two-body

problem, Kepler's laws. Non-inertial (accelerating and rotating) frames of reference. Rigid

bodies (kinematics, dynamics, the inertia tensor). Rotation around a fixed axis, planar motion

of rigid bodies. Torque-free motion of the spherical and symmetric top.


Course title: LabVIEW basics p.c.




Credits (ECTS): 3

Course objectives: The course introduces the students to LabVIEW. Besides being

introduced in the main features of the software through presentations, the students are

required to learn by solving simple problems. By the end of the course, students can write

simple codes for modeling basic physical calculations, and should be able to use the built-in

assistance tools (Help, Example files, etc.) to learn new features.

Course description: Definition, methods and instruments of measurement. Parts of a

LabView monitor: front panel, block diagram, the structure of a vi. The elements of the G

language. Data-flow based, parallel execution. The most important data types. Programming

structures. Creating and including sub-vi-s. LabVIEW VI-library (.llb). Priorities. Timing and

synchronization of different parts of the program. Local and global variables. File I/O.

Implementation of small example codes. Usage of the assistance tools, reading example vi-s.

Assessment methods: oral exam with code implementation

Course title: Physics and electronics lab. II




Credits (ECTS): 4

Course objectives: Acquiring experimental skills, interpretation of measurement data, proper

documentation of measurements.

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course description: 1. Examination of processes with ideal gas. Verification of the gas laws.

2. Measurement of the linear thermal expansion coefficient of solids. Measurement of

the thermal expansion coefficient of fluids.

3. Measurement of the heat capacity of a calorimeter. Measurement of the specific heat

of a solid body with calorimetry.

4. Measurement of the latent heat of melting of ice.

5. Measurement of the heat capacity ratio (cp / cv) of air.

6. Examination of the pressure dependence of the boiling point. Measurement of the

latent heat of boiling of water.

7. Measurement of Joule-Thomson coefficient.

8. Measuring of voltage and intensity of direct current and resistance. Method to measure

the resistance.

9. Ohm’s law, Potentiometer. Resistance measurement by means of Wheatstone-bridge.

Power supplies.

10. The intensity of a coil's magnetic field, force between two current carrying wires.

11. Electric heating. Calibration of temperature sensors. Temperature measurements by

thermo-electric detectors (thermistor and thermocouples). Calorimetry.

12. Study of alternating current resistance. Impedance of R, L, C component.

13. RLC series circuit and resonance. Measurement of the RLC resonance curve


book.

Course title: Lasers and their applications lec.




Credits (ECTS): 2

Course objectives: This subject introduces the students into the world of photonics, deepens

the concepts learned in the frame of „Waves and Optics” and gives examples for scientific

and everyday applications of photonics technologies.

Course description: Absorption and emission of photons. Condition of amplifications.

Linewidth, line shape function, properties of saturation. The principle of matrix optics.

Properties of Gaussian beams. Resonator modes. Rate-equations of lasers. Gas lasers. Solid-

state lasers. Q-switching. Dye lasers and broadband solid-state lasers. Laser tuning.

Semiconductor lasers. Ultrashort pulse lasers. Nonlinear optics in laser physics. Free electron

lasers. Application of lasers.


UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Numerical methods lec.




Credits (ECTS): 2

Course objectives: The students learn about the various numerical methods, their way of

application, and obtain some practice by programming them by themselves.


Course title: Numerical methods p.c.




Credits (ECTS): 3

Course objectives: The students learn about the various numerical methods, their way of

application, and obtain some practice by programming them by themselves.

Assessment methods: Evaluation based on regular assignments.

Course title: Computer programming I p.c.




Credits (ECTS): 3

Course objectives: Introductory course in computer programming. Its aim is to develop the

algorithmic problem solving attitude, and to become able to perform procedural programming

in an imperative language.

Course description: Introduction to scientific programming: formulating mathematical

models of physical problems, construction and implementation of algorithmic models, the

evaluation of the results. Representation of numbers, issues of floating point arithmetics. The

use of the Maple interpreter. Variables. Flow control (conditionals, loops) and their

application in actual problems. Functions and procedures in Maple. Libraries and their

applications. Elements of the C programming language. Types. Flow control. Arrays.

Pointers, pointer arithmetics, dynamical memory allocation. Functions in C. Construction and

compilation of programs with multiple modules. Construction and applications of libraries.

All the issues are introduced through actual problems

Assessment methods: grade based on written exams and homeworks

UNIVERSITY OF PÉCS


Telephone: +36 72 501 500/12418 Fax: +36 72 501 508


Course title: Computer programming II p.c.




Credits (ECTS): 3

Course objectives: Introduction to the basics of object oriented programmig. Development of

the ability to create object oriented console applications

Course description: Objects, classes and namespaces in C#. Basics of object-oriented

programming. Development of console applications with Visual Studio C#.

Assessment methods: Grade based on written exams and homeworks

Course title: Quantum mechanics lec.




Credits (ECTS): 3

Course objectives: to acquire knowledge of quantum behavior and of basic methods of

quantum mechanics


Course title: Quantum mechanics p.c.




Credits (ECTS): 3

Course objectives: to acquire basic knowledge of treating quantum mechanical problems

Course description: Quantum behavior: particles and waves, probability amplitudes. The

wave function as probability amplitude. The time-dependent Schrödinger equation. Stationary

states and the time-independent Schrödinger equation, the Hamilton operator. The position

and the momentum operator. Motion in one-dimensional static potential: step potential,

infinite well, potential barrier. Postulates of quantum mechanics: description of physical state

with wave function or state vector, Hermitian operators as observables, possible results of

measurements and outcome probabilities, collapse of wave function after a measurement.

Mean value of an observable and the root-mean-square deviation. Angular momentum in

quantum mechanics. Spin.

Assessment methods: Written exam at the end of semester

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