# CORE COURSES

1st  SEMESTER

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 power series. Ordinary first-order differential equations: separation of variables, linear. Second-order differential equations: homogeneous, linear with constant coefficients (3,2,0).

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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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2nd  SEMESTER
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.FOREIGN LANGUAGES (A-4)

English, French or German (4,0,0)

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23. LABORATORY COURSES IN MECHANICS (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 = cp/cv of air. (1,0,3)

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24. VECTOR CALCULUS (A-6)

Scalar-valued functions of multiple variables, limits, continuity, partial derivative, differential, directional derivative, extrema, Lagrange multipliers. Vector in Cartesian, cylindrical and spherical coordinates. Vector transformation under rotation of the coordinate system. Vector products and vector identities. Vector and dot products and vector calculus identities. Curves, trihedron Frenet, surfaces. Differential calculus of scalar and vector fields: Directional derivative, gradient, vector differential operator, divergence, curl, Laplacian, product rules (in Cartesian, cylindrical and spherical coordinates). 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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3rd  SEMESTER

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. (4,1,0)

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33. CLASSICAL MECHANICS I (A-6)

Principles of Newtonian Mechanics. Statics. Dynamics. Conservation of momentum, angular momentum and energy. Potential – Conservative forces. Coupled and non-linear oscillators, three-dimensional harmonic oscillator. Collisions – systems of variable mass. Central potential. Trajectories in gravitational potential, Kepler’s laws, stationary solutions. Elastic scattering. Gravitational fields of finite body. (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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4th  SEMESTER

41. THERMODYNAMICS AND LABORATORIES IN HEAT (A-7)

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, 1st thermodynamic law, heat capacities Cp, Cv, adiabatic transition equation, applications of the 1st 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, 2nd thermodynamic law, thermal engines, Kelvin-Planck formulation, Clausius formulation, equivalence of formulations. Carnot cycle, introduction of absolute temperature, Clausius theorem, entropy, Karatheodory formulation, Clausius inequality, principle of entropy. Calculation of changes in entropy. Entropy and disorder, absolute zero, negative temperatures, 3rd 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.  (3,1,1)

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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-6)

Non-inertial reference frames. 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. DIFFERENTIAL EQUATIONS (A-6)

Ordinary first-order differential equations. Simple second-order differential equations, Newton’s equation, applications. Solution methods for equations with constant coefficients. Fourier series, Laplace transform, applications. Partial differential equations. Variable separation method, series solutions, Frobenius method. Known classical functions as solutions of differential equations. Applications of differential equations in physics. Simple systems of differential equations (3,2,0)

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5th  SEMESTER
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)

Historical facts, the evolution of chemistry, the importance of chemistry in the modern world, the contribution of physics to chemistry. Chemical language and calculations: symbolism in chemistry, nomenclature, periodic table, mole & molecular weight, valence, stoichiometry. Basic inorganic chemistry: types of inorganic reactions, catalysis, industrial reactions, metallurgy, environment, technology of air and water, inorganic materials of state-of-the-art technology, nuclear chemistry (radioisotopes, nuclear fission/fusion, energy of nuclear reactions). Basic organic chemistry: nomenclature, homologous series, petrochemistry, classic organic reactions, polymers, thermochemistry (fuels, explosive materials), molecular geometry-carbon, quantum models and applications in organic chemistry (particle-in-a-box, quantum tunneling), organic chemistry in everyday life. Chemical technology: ceramic-building materials, energy-fuels, explosives, products in everyday life. (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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6th  SEMESTER

61. QUANTUM THEORY II (A-7)

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-7)

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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7th  SEMESTER

71. STATISTICAL PHYSICS I (A-7)

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-7)

Introduction. Crystal structure (lattice, Bravais lattices, simple crystal structures, non-crystalline structures-glasses). Reciprocal lattice (diffraction, Bragg,’s law, von Laue equations and their equivalence). Amplitude of the diffracted wave, Brillouin zones, geometrical and atomic structure factor. Classification of solids- lattice types-Mechanical Properties. Inert gas crystals, ionic-covalent-metallic Crystals. Phonons-Lattice vibrations. Strain, stress, elastic modulus, compressibility. Phonons- Thermal Properties. Phonon specific heat capacity (Einstein model, Debye). Anharmonicity, thermal conductivity. Metals (free electron model, Drude model, Sommerfield, Fermi-Dirac distribution, successes and failures of the models). Electric conductivity of metals, dielectric constant, plasma frequency, motion in magnetic field, thermal conductivity. Electronic states in periodic potential. Bloch theorem, Kronig-Penney. Model. Formation of energy gap, energy bands, metals and insulators. Electrons in weak periodic potential. Electron energy states close to Bragg’s reflection condition, Fermi energy and Brillouin zones, effective mass. Semiconductors. Equations of motion, concentration and mobility of carriers, electrical properties controlled by impurity addition, p-n junctions (solar cells, photovoltaics) (3,1,0)

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