**11. MECHANICS (A-7)**

Motion in one dimension. Motion in two dimensions. Particle dynamics. Work and energy. Energy conservation. Momentum conservation. Particle collisions. Kinematics of rotation. Angular momentum conservation. Rigid bodies. Oscillations. Gravitational force. Fluid statics and dynamics. (4, 1, 0)

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**12. DIFFERENTIAL AND INTEGRAL CALCULUS (A-7)**

Real functions of one variable. Limits and continuity. Derivative and differential. Applications of derivatives. Indefinite, definite and improper integral. Applications of integrals. Sequences, series, power series, Taylor and Maclaurin power series. Functions with many variables, partial derivatives, total differential, and their applications in Physics. Implicit differentiation, Leibniz’s rule. Extremal and saddle points, Lagrange multipliers, applications. (4,2,0)

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**13. LINEAR ALGEBRA AND ELEMENTS OF ANALYTICAL GEOMETRY (A-6)**

Basic vector algebra. Matrices, determinants, solution of system of linear equations. Eigenvalues, eigenvectors, diagonalization of matrices with examples from Physics. Algebra of complex numbers, Euler’s formula, root determination, applications. Basic concepts of Analytical geometry in Cartesian and polar coordinates. Equations of line, conic sections, plane and sphere. Equations of second degree on the plane and in three-dimensional space. (4,1,0)

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**14. INTRODUCTION TO COMPUTERS (A-5)**

General description of computer structure. Hardware. Software. DOS, UNIX operational systems. WINDOWS platform. Text editors. Spreadsheets. Graphics and data analysis. Algorithms. (2,0,2)

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**15. ELEMENTS OF PROBABILITIES AND STATISTICS (A-5)**

The role of probability in Physics. Statistical description of measurements. Simple combination and applications. Probability definitions. Conditional probability and Bayes formula. Random variables and probability distributions. Parameters of distributions. Basic theoretical distributions (geometrical, binomial, Poisson, normal, Maxwell, etc.) and applications. Elements of error theory, parameter evaluation and fitting. (3,0,1)

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**21. ELECTROMAGNETISM (A-7)**

Electric charge. Electric field and Gauss law. Electric potential. Capacitors and dielectrics. Electric properties of matter. Electric current and resistance. Electromotive force and circuits. Magnetic field. Biot-Savart and Ampere-Faraday law. Self-induction. Magnetic properties of matter. Alternating current and RCL circuits. Maxwell equations and electromagnetic waves. (4,1,0)

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**22. DIFFERENTIAL EQUATIONS (A-6)**

Ordinary first-order differential equations. Second order differential equations, Newton formula, applications. Special methods for equations with constant factors, Fourier series, Laplace transformations, applications. Partial differential equations. Separation of variables, series solutions, Frobenius method. Basic functions as solutions to differential equations. Applications of partial differential equations in physics. Simple systems of differential equations. (3,2,0)

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**23. LABORATORY COURSES IN MECHANICS AND HEAT (A-6)**

Mechanics: Instruments for measurement of basic quantities, length-mass-time. Measurement of velocity and acceleration. Study of rectilinear and accelerated motion. Newton’s law. Impulse-Momemtum, momentum conservation – collisions. Work-Energy, Energy conservation. Study of circular motion. Oscillations, harmonic, digressive and forced oscillation. Fluids, measurement of the thickness of fluids and solids via buoyancy, motion of solids in liquids. Heat: Thermal expansion of solids and liquids. Calorimetry, measurements of the specific heat of solids and liquids. Mechanical equivalent of heat. Measurement of the ratio γ = c_{p}/c_{v} of air. (1,0,3)

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**24. VECTOR CALCULUS (A-6)**

Vector in Cartesian, cylindrical and spherical coordinates. Vector transformation under rotation of the coordinate system. Vector products and vector identities. Motion of a point particle on a plane. Differential calculus of scalar and vector fields: Directional derivative, gradient (in Cartesian, cylindrical and spherical coordinates), vector differential operator, divergence, curl, Laplacian, product rules. Double, triple integrals and applications. Change of variables and Jacobian determinant. Line and surface integrals. Fundamental integral theorems for the gradient, divergence and curl with applications in Physics. (3,1,0)

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**25. PROGRAMMING LANGUAGES (A-5)**

Introduction to C programming language. Introduction to Linux. Simple input-output command lines, formulas, operators. Flow command lines. Program functions and structure. Matrices. Structures. (2,0,2)

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**31. WAVES (A-6)**

Waves in elastic media. Wave types, wave quantities, wave equation. Harmonic waves. Interference, standing waves, dispersion. Transmission velocity in elastic media. Resistance of medium. Acoustic waves. Maxwell equations and electromagnetic waves. Nature and propagation of light. Interference, diffraction, spectra. Reflection, refraction. Polarization, birefringence. (4,1,0)

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**32. MODERN PHYSICS I (A-6)**

Relativity theory: Galileo transformations. The Michelson-Morley experiment. Special Relativity. Lorentz transformations. Energy and momentum. Elements of General Relativity. Quantum-mechanics: black-body radiation. Photoelectric effect. Compton effect. Pair production and annihilation. The Bohr model of the atom. The Davison-Germer experiment. De Broglie waves. Heisenberg uncertainty principle. Wavefunctions. Schroedinger equation. (3,1,0)

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**33. CLASSICAL MECHANICS I (A-6)**

Principles of Newtonian Mechanics. Statics. Dynamics. Potential – Conservative forces. Conservation of momentum and energy. Collisions – systems of variable mass. Coupled oscillators. Central potential. Kepler’s problem, trajectories in gravitational potential, stationary solutions. Three-dimensional harmonic oscillator. Elastic scattering. Non-inertial reference systems (3,1,0)

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**34. COMPLEX NUMBERS CALCULUS AND INTEGRAL TRANSFORMATIONS (A-6)**

Functions of a complex variable, Cauchy-Riemann conditions, analytic functions, harmonic functions. Elementary complex functions: Exponential, logarithmic, trigonometric and their inverse functions. Loop integrals. Cauchy-Goursat theorem. Cauchy integral formula. Laurent series. Integral residuals and methods for their calculation. Applications of integral residuals. Analytical continuation. Fourier integrals. Elements of generalized functions, the δ(x) distribution function. Elements of Hilbert spaces. (3,2,0)

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**35. LABORATORY COURSES IN ELECTROMAGNETISM (A-6)**

Experiments in electromagnetism: electric current, resistance measurement, electromotive force, electrical power, ohmmeter, galvanometer. Zero measurement methods and bridges. Potentiometers. Magnetic field, induction. Oscilloscope. Transition phenomena. Alternating current. RC, RL, RCL circuits. Impedance. Frequency filters. (1,0,3). __21 (this prerequisite is compulsory)__

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**41. THERMODYNAMICS (A-6)**

Basics, macroscopic/microscopic approach, definition and measurement of temperature, temperature of ideal gas, state functions, perfect differentials, thermodynamic equilibrium. Work in hydrostatic and non-hydrostatic systems, reversible and non-reversible transitions, 1^{st} thermodynamic law, heat capacities Cp, Cv, adiabatic transition equation, applications of the 1^{st} thermodynamic law (velocity of a longitudinal wave, free expansion). Equation of state of non-ideal gas, Virial equation, deviation from the ideal case, deviation factor Z. Heat-work conversions, 2^{nd} thermodynamic law, thermal engines, Kelvin-Planck formulation, Clausius formulation, equivalence of formulations. Carnot cycle, introduction of absolute temperature, Clausius theorem, entropy, Karatheodoris formulation, Clausius inequality, principle of entropy. Calculation of changes in entropy. Entropy and disorder, absolute zero, negative temperatures, 3^{rd} thermodynamic law. Thermodynamic potentials, maximum work gain, fundamental equation of thermodynamics, Maxwell equations, TdS equations, equations of heat capacities. Refrigeration of gases, Joule-Thomson expansion (enthalpy), phase equilibrium, equilibrium condition, Clausius-Clapeyron equation. Qualitative and quantitative diagrams P-V and P-T, critical point, g-T and g-P diagrams. Chemical potential, heat transfer. (3,1,0)

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**42. MODERN PHYSICS II (A-7)**

Atomic structure: the Hydrogen atom. Electron spin. Stern-Gerlach experiment. Multielectron atoms. Pauli exclusion principle and periodic system. Stimulated light emission and laser. Molecules and solids: molecular bonds. Spectra of diatomic molecules. Basics of band theory and conduction. Nuclear structure: classification of nuclei. Nuclear structure models. Alpha and beta decay. Fission and fusion. Elementary particles: fundamental forces. Particle classification. The Standard model description. (4,1,0)

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**43. CLASSICAL MECHANICS II (A-7)**

Rigid body mechanics: Systems of point particles and continuous systems, inertia tensor, principal axes, Euler equations. Calculus of variations, the ‘brachistochrone’ problem. Lagrange formalism: generalized coordinates, equations of motion, conserved quantities, Noether theorem. Hamilton formalism: canonical equations, phase-space. Poisson brackets. Canonical transformations. (3,1,0)

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**44. LABORATORY COURSES IN WAVE PHYSICS AND OPTICS (A-6)**

Light optics: reflection, refraction, polarization, dispersion, interference, diffraction, wave length and light velocity, lenses, optical fibers, holography, optical spectroscopy, emission spectra, absorption spectra. Microwaves: Intensity distribution, reflection, refraction, polarization, interference, diffraction, optical waveguides. Ultrasonic acoustics: spectral distribution, intensity distribution, wave length, transmission velocity, interference, diffraction. (1,0,4)

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**45. FOREIGN LANGUAGE (A-4)**

The student chooses one of the offerd by the Department foreign languages (English/French/German).

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**51. QUANTUM THEORY I (A-7)**

Basic concepts: probability amplitude, operators, wavefunction. Schrödinger equation. One-dimensional potentials. Simple two-state systems. Harmonic oscillator. Symmetries. Angular momentum, spin. (3,1,0)

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**52. CLASSICAL ELECTRODYNAMICS I (A-7)**

Electrostatic field and potential function. Work and energy in electrostatics. General methods for calculating the potential. Electrostatic fields in matter. Magnetostatic field and vector potential. Magnetostatic fields in matter. (3,1,0)

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**53. ANALOG ELECTRONICS (A-6)**

Principles of circuit theory, semiconductors, PN junction, properties. Solid state diodes (zener, varicap, LASER, LED, photodiodes, etc.), operation, circuits and applications. Dipole transistors, equivalent circuits, transfer models. FET, study, analysis, applications. Amplifiers with transistors, models for small signal amplification. FET amplifiers. Amplifiers of multiple outputs. (A,B,AB,C,D). Current supplies, active loads. Thyristor, Diac, Triac, UJT, etc, analysis, operation, applications. Circuit transfer functions, determinations of zero poles. Frequency response of amplifiers. Differential amplifier, study, analysis, operation. Operational amplifier, ideal, non-ideal. Applications of operational amplifiers, special circuits. Active filters, study, applications. Transistor models for high frequencies. (2,1,2)

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**54. GENERAL CHEMISTRY (A-5)**

Historic elements. Laws of Chemistry. Electronic structure of the atoms and the periodic table of elements. Lewis theory. VSEPR theory. Molecular orbitals. σ, π and δ bonds. Acids, Bases and Salts. Properties of acids, bases, neutralization, reactions of double replacement. Chemical kinetics. Chemical balance. Bidirectional reactions. Factors affecting the chemical balance, Le Chatelier principle. Constant of chemical balance – Degree of ionization. Water ionization – pH. Indexes, cubage. Solubility product. Oxidation reduction – Electrochemistry. Introduction to the chemistry of composite compounds. Organic chemistry. Classification of organic compounds, nomenclature. Isomerism. Hydrocarbons (alkanes, alkenes, alkines, benzol). Alcohols, phenols, ethers. Carbonylic compounds. Carboxylic acids and products. Elements of mechanisms of organic reactions. (3,1,0)

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**405. ENVIRONMENTAL PHYSICS (A-5)**

Planet Earth and the origins of its environment. Formation of solid, liquid and gaseous elements. The terrestrial atmosphere, hydrosphere and lithosphere. Physical principles of environmental problems. Natural forces. Air pollution. Atmospheric cycles of basic forms of waste. Chemical reactions of gaseous pollutants. Atmospheric ozone. Ozone layer hole. Size distributions of particles. Mechanisms of removal of atmospheric pollutants. Boundary layer. Mixing-length theory. Turbulent flow. Reynolds number. Air pollution and Meteorology. Models of transport, diffusion and deposition. Influence of temperature stratification on diffusion. Influence of meteorological parameters. Pollution drains. Acid rain. Influence of pollution on weather and climate. Influence of pollution on health, plant and animal environment. Radioactive pollution. Noise pollution. Physics and pollution of water (sea, lake, river). Diluted gases. Chemical cycles. Chemical reactions. Bacteriological water pollution. Chemical pollution. Energy and pollution. Environmental impact. Physics and soil pollution. (3,1,0)

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**408. INTRODUCTION TO ASTROPHYSICS (A-5)**

Mechanisms of emission and absorption of radiation. Radiation transfer. Stellar magnitudes and distances. Stellar spectra and classification, Hertzsprung-Russell diagram. Internal structure, formation and evolution of stars. Final states: white dwarfs, neutron stars and black holes. The sun and the solar system. Variable and singular stars. Stellar groups and clusters. Interstellar matter. Our Galaxy. Cosmology. (3,1,0)

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**61. QUANTUM THEORY II (A-8)**

Central potential. Hydrogen-like atoms. Degeneracy. Fine and hyperfine structure. Perturbation theory. Scattering theory. Identical particles. Pauli's principle. (3,1,0)

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**62. CLASSICAL ELECTRODYNAMICS II (A-8)**

Faraday law. Maxwell equations. Energy and momentum in electrodynamics. Electromagnetic waves in conductive and non-conductive media. Dispersion. Guided waves. Electric and magnetic dipole radiation. Point-charge radiation. Basic concepts of relativity in electrodynamics. (3,1,0)

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**71. STATISTICAL PHYSICS I (A-8) **

Overview of classical thermodynamics. Statistical thermodynamics of an isolated system. Thermal systems with constant number of molecules. Classical statistical mechanics. Thermal systems with variable number of molecules. Statistics of identical particles. (3,1,0)

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**72. SOLID STATE PHYSICS I (A-8)**

Theory of free electron. X-ray diffraction. Crystal lattices and structure. Theory of Bloch electrons, Energy bands. Simple methods for calculating and measuring energy bands. Dynamics of Bloch electrons, active mass, holes, transfer phenomena. (3,1,0)

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