# Curricula and Syllabi of FNSPE CTU in Prague

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## Aktualizace dat: 15.10.2017

Bachelor degree programmeDosimetry and Applications of Ionising Radiation
Year 2
course code teacher ws ss ws cr. ss cr.

## Compulsory courses

Calculus A301MAA34 Vrána 4+4 z,zk 4+4 z,zk 10 10
 Course: Calculus A3 01MAA3 Ing. Fučík Radek Ph.D. / Ing. Vrána Leopold 4+4 Z,ZK - 10 - Abstract: Function sequences and series, foundation of topology, and differential calculus of several variables. Outline: Function sequences and series: Pointwise and uniform convergence, interchange rules for limits, derivatives and integrals. Fourier's series, expansion of a function into trigonometrical series, tests for pointwise and uniform convergence of trigonometrical series, completeness of trigonometric system. Topology of normed linear space, compact, connected and complete sets, fixpoint theorem. Differential calculus of several variables: directional derivatives, partial and total derivatives, mean-value theorems, extremum, manifolds, constrained extrema. Outline (exercises): Uniform convergence. Interchange rules. Expansion of a function into trigonometrical series. Directional derivative. Total derivative. Local extrema. Goals: To acquaint the students with the properties of function sequences and series, expansion of a function into trigonometrical series, with an introduction to the topology, and with foundation of differential calculus of several variables. Requirements: Basic Course of Calculus and Linear Algebra (in the extent of the courses 01MA1, 01MAA2, 01LA1, 01LAA2 held at the FNSP CTU in Prague). Key words: Function sequences and series, Fourier's series, topological and metric space, compactness, connectness, completeness, total derivative, local extrema. References Key reference: W.H.Fleming,Functions of Several Variables, Addison-Wesley, Reading, MA, 1966. Recommended references: Mariano Giaquinta, Giuseppe Modica, Mathematical Analysis - An Introduction to Functions of Several Variables, Birkhäuser, Boston, 2009

 Course: Calculus A4 01MAA4 Ing. Vrána Leopold - 4+4 Z,ZK - 10 Abstract: Integration of functions of several variables, measure theory, foundation of differential and integral calculus on manifolds and complex analysis. Outline: Lebesgue integral: Daniel?s construct, interchange rules, measurable sets and measurable functions. Fubini's theorem, theorem on changing variables. Parametrical integrals: Interchange theorems, Gamma and Beta functions. Differential forms: conservative, exact and closed form and their relations, potential. Line and surface integral: Green's, Gauss' and Stokes' theorem. Complex analysis: analytic functions, Cauchy's theorem, Taylor's expansion, Laurent's expansion, singularities, residue theorem. Outline (exercises): Smooth manifolds. Constrained extrems. Differential forms. Lebesgue integral in several variables. Use of Fubini's theorem and theorem on changing variables. Use of Gamma and Beta functions for computation of integrals. Computation of integrals Goals: To acquaint the students with foundations of Lebesgue integration and with foundations of complex analysis and its use in applications. Requirements: Basic Course of Calculus and Linear Algebra (in the extent of the courses 01MA1, 01MAA2-3, 01LA1, 01LAA2 held at the FNSP CTU in Prague). Key words: Lebesgue integral, measurable functions and sets, Gamma and Beta functions, line and surface integral, divergence theorem, Cauchy's theorem, residue theorem. References Key reference: W.H.Fleming,Functions of Several Variables, Addison-Wesley, Reading, MA, 1966. Recommended references: Mariano Giaquinta, Giuseppe Modica, Mathematical Analysis - An Introduction to Functions of Several Variables, Birkhäuser, Boston, 2009

Numerical Mathematics 101NUM1 Oberhuber 3+1 z,zk - - 4 -
 Course: Numerical Mathematics 1 01NUM1 Ing. Oberhuber Tomáš Ph.D. 3+1 Z,ZK - 4 - Abstract: The course introduces to numerical methods for solving the basic problems arising from technical and research problems. The accent is put on a good understanding of the root of theoretical methods. Outline: 1. Recapitulation of necessary concepts from linear algebra and functional analysis. 2. Direct and iterative methods for solving linear algebraic equations. Matrix inversion. 3. Solving the partial eigenvalue problem. 4. Solution of the full eigenvalue problem. 5. Solving the equation f (x) = 0 6. Systems of nonlinear algebraic and transcendental equations. 7. Interpolation functions by polynomials. 8. Numerical calculation of derivatives. 9. Numerical calculation of integral Outline (exercises): 1. Practicing rules of operations with triangular matrices, proofs of theorems on decompositions of square matrices, derivation of decomposition formulae. 2. Proof of Schur decomposition theorem. Consequences for special classes of matrices. 3. Examples of solution of systems of linear algebraic equations and matrix inversion using direct methods. 4. Examples of solution of systems of linear algebraic equations using iterative methods. 5. Examples of application of methods for solution of extremal eigenvalues and complete eigenvalue problem. 6. Examples of solution of non-linear algebraic and transcendental equations and their systems. Numerical approximation of integrals. Goals: Knowledge: Correct understanding of the theoretical basis for numerical algorithms is accented. Skills: Applications of numerical methods for solution of basic mathematical tasks originated from technical or scientific problems. Requirements: Key words: Direct methods, iterative methods, eigenvalue problem, systems of equations, interpolation, numerical calculation of integrals References Key references: [4] A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics. Springer-Verlag 2000 Recommended references: [5] A. S. Householder: The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Company 1965

Differential Equations01DIFR Beneš - - 2+2 z,zk - 4
 Course: Differential Equations 01DIFR prof. Dr. Ing. Beneš Michal - 3+1 Z,ZK - 4 Abstract: The course contains introduction in the solution of ordinary differential equations. It contains a survey of equation types solvable analytically, basics of the existence theory, solution of linear types of equations and introduction in the theory of boundary-value problems. Outline: 1. Introduction - motivation in applications 2. Basics - theory of ordinary differential equations 3. Particular types of 1st-order ODEs. - separated and separable equations - homogeneous equations - equations with the rational argument of the righthand side - linear equations - Bernoulli equations - Riccati equations - Equations x=f(y') a y=f(y') 4. Existence theory for equations y'=f(x,y) - Peano theorem - Osgood theorem 5. Sensitivity on the righthand side and on the initial conditions 6. Linear n-th order differential equations 7. Systems of 1st order linear differential equations 8. Boundary-value problems Outline (exercises): 1. Equations with separated variables 2. Separable equations 3. Homogeneous differential equations 4. Generalized (quasi-homogeneous) differential equations 5. Equations with rational righthand-side argument s racionálním argumentem 6. Linear 1st-order differential equations 7. Bernoulli equations 8. Riccati equations 9. Differential equations x=f(y') a y=f(y') 10. Linear n-th order differential equations with constant coefficients 11. Fundamental system for linear n-th order differential equations 12. Systems of linear 1st order differential equations with constant coefficients Goals: Knowledge: analytical solution of selected types of equations, the basics of the existence theory, solution of linear types of equations Skills: Analytical solution of the known types of ordinary differential equations, mathematical analysis of the initial-value problems, solution of linear n-th order differential equations and of the system of 1st-order linear ordinary differential equations. Requirements: Basic course of Calculus, Linear Algebra (in the extent of the courses 01MA1, 01MAA2-4, 01LA1, 01LAA2 held at the FNSPE CTU in Prague). Key words: Initial-value problems for differential equations, Euler approximation, Peano theorem, fundamental system, wronskian, method of variation of constants. References Key references: [1] J. Kluvánek, L. Mišík a M. Švec. Mathematics II, SVTL Bratislava 1961 (in Slovak) [2] K. Rektorys a kol. Survey of Applied Mathematics, Prometheus, Praha 1995 (in Czech) Recommended references: [3] L. S. Pontryagin, Ordinary Differential Equations. Addison-Wesley, London 1962 [4] A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, Chapman and Hall/CRC Press, Boca Raton, 2003 [5] M.W.Hirsch, S.Smale, Differential Equations, Dynamical systems, and Linear Algebra, Academic Press, Boston, 1974 [6] F.Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, Berlin 1990 [7] W. Walter, Gewöhnliche Differenzialgleichungen, Springer, Berlin 1990

Calculus B301MAB34 Krbálek 2+4 z,zk 2+4 z,zk 7 7
 Course: Calculus B3 01MAB3 doc. Mgr. Krbálek Milan Ph.D. 2+4 Z,ZK - 7 - Abstract: The course is devoted to functional sequences and series, theory of ordinary differential equations, theory of quadratic forms and surfaces, and general theory of metric spaces, normed and prehilbert?s spaces. Outline: 1. Functional sequences and series - convergence range, criteria of uniform convergence, continuity, limit, differentiation and integration of functional series, power series, Series Expansion, Taylor?s theorem. 2. Ordinary differential equations - equations of first order (method of integration factor, equation of Bernoulli, separation of variables, homogeneous equation and exact equation) and equations of higher order (fundamental system, reduction of order, variation of parameters, equations with constant coefficients and special right-hand side, Euler?s differential equation). 3. Quadratic forms and surfaces - regularity, types of definity, normal form, main and secondary signature, polar basis, classification of conic and quadric 4. Metric spaces - metric, norm, scalar product, neighborhood, interior and exterior points, boundary point, isolated and non-isolated point, boundary of set, completeness of space, Hilbert?s spaces. Outline (exercises): 1. Functional sequences. 2. Functional series. 3. Power series 4. Solution of differential equations. 5. Quadratic forms. 6. Quadratic surfaces. 7. Metric spaces, normed and Hilbert?s spaces. Goals: Knowledge: Investigation of uniform convergence for functional sequences and series. Solution of differential equations. Classification of quadratic forms and surfaces. Classification of points of sets. Skills: Individual analysis of practical exercises. Requirements: Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01LA1, 01LAB2 held at the FNSPE CTU in Prague). Key words: Function sequences, function series, differential equations, quadratic forms, quadratics surfaces, metric spaces, norm spaces, pre-Hilbert spaces References Key references: [1] Robert A. Adams, Calculus: A complete course, 1999, [2] Thomas Finney, Calculus and Analytic geometry, Addison Wesley, 1996 Recommended references: [3] John Lane Bell: A Primer of Infinitesimal Analysis, Cambridge University Press, 1998 Media and tools: MATLAB

 Course: Calculus B4 01MAB4 doc. Mgr. Krbálek Milan Ph.D. - 2+4 Z,ZK - 7 Abstract: The course is devoted properties of functions of several variables, differential and integral calculus. Furthermore, the measure theory and theory of Lebesgue integral is studied. Outline: Differential calculus of functions of several variables - limit, continuity, partial derivative, directional partial derivative, total derivative and tangent plane, Taylor?s theorem, elementary terms of vector analysis, Jacobi matrix, implicit functions, regular mappings, change of variables, non-cartesian coordinates, local and global extremes. Integral calculus of functions of several variables - Riemann?s construction of integral, Fubiny theorem, substitution of variables. Curve and surface integral - curve and curve integral of first and second kind, surface and surface integral of first and second kind, Green and Gauss and Stokes theorems. Fundamentals of measure theory - set domain, algebra, domain generated by the semi-domain, sigma-algebra, sets H_r, K_r and S_r, Jordan measure, Lebesgue measure. Abstract Lebesgue integral - measurable function, measurable space, fundamental system of functions, definition of integral, Levi and Lebesgue theorems, integral with parameter, Lebesgue integral and his connection to Riemann and Newton integral, theorem on substitution, Fubiny theorem for Lebesgue integral. Outline (exercises): 1. Function of several variables (properties). 2. Function of several variables (differential calculus). 3. Function of several variables (integral calculus) 4. Curve and surface integral. 5. Measure Theory 6. Theory of Lebesgue integral. Goals: Knowledge: Investigation of properties for function of severable variables. Multidimensional integrations. Curve and surface integration. Theoretical aspects of measure theory and theory of Lebesgue integral. Skills: Individual analysis of practical exercises. Requirements: Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01MAB3, 01LA1, 01LAB2 held at the FNSPE CTU in Prague). Key words: Function of several variables, curve and surface integrals, measure theory, theory of Lebesgue integral References Key references: [1] M. Giaquinta, G. Modica, Mathematical analysis - an introduction to functions of several variables, Birkhauser, Boston, 2009 Recommended references: [2] S.L. Salas, E. Hille, G.J. Etger, Calculus (one and more variables), Wiley, 9th edition, 2002 Media and tools: MATLAB

Numerical Methods 112NME1 Limpouch - - 2+2 z,zk - 4
 Course: Numerical Methods 1 12NME1 prof. Ing. Limpouch Jiří CSc. - 2+2 Z,ZK - 4 Abstract: There are explained the basic principles of numerical mathematics important for numerical solving of problems important for physics and technology. Methods for solution of tasks very important for physicists (ordinary differential equations, random numbers) are included in addition to the basic numerical methods. Integrated computational environment MATLAB is used as a demonstration tool. The seminars are held in computer laboratory and PASCAL is used as a principle programming language and MATLAB is also used. Outline: 1.Numerical mathematics, truncation error, floating point representation of numbers, roundoff error 2.Correctness of problem, condition number, numerical stability; numerical libraries 3.Solution of linear equation systems - direct methods 4.Sparse matrices, iteration methods for linear equation systems; eigensystems 5.Interpolation and extrapolation, interpolation in more dimensions 6.Chebyshev approximation, Chebyshev polynomials, least square approximation 7.Evaluation of functions; sorting 8.Root finding and nonlinear set of equations 9.Search for extremes of functions 10.Numerical integration of functions 11.Random numbers and Monte Carlo integration 12.Ordinary differential equations - initial problem, stiff equations 13.Ordinary differential equations - boundary value problem Outline (exercises): The seminars are held in computer laboratory and PASCAL is used as a principle programming language and system MATLAB is applied for demonstrations. 1. Floating point representation of numbers, roundoff error, condition number 2.Solution of linear equation systems - direct methods, condition number of matrix 3.Sparse matrices, iteration methods for linear equation systems; eigensystems 4.Interpolation and extrapolation, cubic spline 5.Chebyshev approximation, Chebyshev polynomials, least square approximation 6.Evaluation of functions 7.Root finding and nonlinear set of equations 8.Search for extremes of functions 9.Numerical integration of functions 10.Ordinary differential equations - initial problem, stiff equations 11.Ordinary differential equations - boundary value problem Goals: Knowledge: Basic principles of numerical mathematics important for numerical solving of problems important for physics and technology including also ordinary differential equations. Skills: Usage of numerical mathematics for solving of practical problems, ability to choose routines from numerical libraries and to avoid most common errors. Requirements: Key words: Applied numerical mathematics, PASCAL language, MATLAB, ordinary differential equations. References Key references: [1] W.H. Press, B.P. Flannery, S.A. Teukolsky, V. H. Vetterling: Numerical Recipes in Pascal (The art of scientific computation), Cambridge University Press, Cambridge 1989 (also versions for C and Fortran). Recommended references: [2] A. Ralston, P. Rabinowicz, A First Course in Numerical Analysis, McGraw-Hill 1965 (reprinted by Dover Publiícations, 2001) [3] R.W. Hamming, Numerical Methods for Scientists and Engineers, 2nd edition, Dover Publiícations 1986 Equipment: Computer laboratory with Pascal programming language and Matlab program.

Selected Topics in Mathematics01VYMA Mikyška - - 2+2 z,zk - 4
 Course: Selected Topics in Mathematics 01VYMA doc. Ing. Mikyška Jiří Ph.D. - 2+2 Z,ZK - 4 Abstract: Fourier series: complete orthogonal systems, expansion of functions into Fourier series, trigonometric Fourier series and their convergence. Complex analysis: derivative of holomorphic functions, integral, Cauchy's theorem, Cauchy's integral formula, singularities, Laurent series, residue theorem. Outline: 1. Theory of Fourier series in a general Hilbert space, complete orthogonal systems, Bessel inequality, Parseval equality. 2. Fourier series in L2, trigonometric system, Fourier coefficients, Bessel inequality, Parseval equality, expansion of a function into trigonometric series. 3. Criteria of convergence of Fourier series. 4. Analysis of complex functions: derivative, analytical functions, Cauchy-Riemann conditions. 5. Contour integral of complex functions of a complex variable, theorem of Cauchy, Cauchy's integral formula. 6. Expansion of an analytic function into a power series, isolated singularities, Laurent expansion, residue theorem. Outline (exercises): 1. Summary of properties of function series, investigation of the uniform convergence of function series. 2. Fourier series in a general Hilbert space, Gramm-Schmidt ortogonalization, ortogonal polynomials. 3. Trigonometric system in L2. Expansions of trigonometric functions into trigonometric Fourier series, investigation of convergence of the trigonometric series. Summation of some series using the Fourier expansions. 4. Elementary functions of complex variables: polynomials, exponential function, goniometric functions, complex logarithm 5. Analysis in a complex domain: continuity, derivative, Cauchy-Riemann conditions. 6. Evaluation of contour integrals of complex functions of a complex variable, applications of the Cauchy theorem, Cauchy integral formula and residue theorem. Goals: Expansion of functions to the Fourier series and investigation of their convergence, application of theory of analytic functions for evaluation of curve integrals in complex plane and evaluation of some types of definite integral of real functions of a real variable. Skills: to use expansions of functions into a Fourier series to evaluate sums of some series, evaluation of definite integrals using the theory of functions of complex variable. Requirements: Basic Calculus (in the extent of the courses 01MA1, 01MAA2-3, or 01MAB2-3 held at the FNSPE CTU in Prague). Key words: Sequences and series of functions, Fourier series, complex analysis. References Key references: [1] J. Dunning-Davies, Mathematical Methods for Mathematicians, Physical Scientists and Engineers, John Wiley and Sons Inc., 1982. Recommended references: [2] A. S. Cakmak, J. F. Botha, and W. G. Gray, Computational and Applied Mathematics for Engineering Analysis, Springer-Verlag Berlin, Heidelberg, 1987.

Waves, Optics and Atomic Physics02VOAF Tolar 4+2 z,zk - - 6 -
 Course: Waves, Optics and Atomic Physics 02VOAF prof. Ing. Tolar Jiří DrSc. 4+2 Z,ZK - 6 - Abstract: Wave phenomena in mechanics and electromagnetism: modes, standing and travelling waves, wave packets in dispersive media. Wave optics: polarization, interference, diffraction, coherence. Geometrical optics. Atomic physics: black body radiation, quantum of energy, photoeffect, the Compton effect, the de Broglie waves, atomic spectra and the structure of atoms. Outline: 11. Oscillations of systems of mass points 2. Travelling waves in non-dispersive media 3. Waves in dispersive media 4.-5. Energy and reflection of waves 6. Electromagnetic waves 7. Polarization 8. Interference and diffraction 9. Geometrical optics 10. Black body radiation, photons 12. de Broglie waves 13. Spectra and stationary states of atoms Outline (exercises): Solving examples on the following topics: 1. Oscillations of systems of mass points 2. Travelling waves in non-dispersive media 3. Waves in dispersive media 4.-5. Energy and reflection of waves 6. Electromagnetic waves 7. Polarization 8. Interference and diffraction 9. Geometrical optics 10. Black body radiation, photons 12. de Broglie waves 13. Spectra and stationary states of atoms Goals: Knowledge: Physics of mechanical and electromagnetic oscillations and waves, foundations of atomic physics. Skills: Solving concrete physical and technical examples concerning oscillations and waves. Requirements: Course of basic physics (02MECH, 02ELMA) Key words: oscillations, standing waves, travelling waves, plane waves, dispersion relation, quasimonochromatic wave packets, phase velocity, group velocity, characteristic impedance, energy density, energy flux density, reflectivity, radiation pressure, polarization of light, interference, diffraction grid, diffraction on References Key references: [1] F.S. Crawford, Jr.: Berkeley Physics Course 3, Waves, McGraw-Hill, New York 1968 [2] J. Tolar, J. Koníček: Sbírka řešených příkladů z fyziky (Vlnění), skripta ČVUT, Praha 1999 Recommended references: [3] J. Tolar: Vlnění, optika a atomová fyzika, kap. 1. - 9., viz //www.fjfi.cvut.cz, katedra fyziky [4] H. Georgi: The Physics of Waves, Prentice Hall, Upper Saddle River NJ 1993

Thermodynamics and Statistical Physics02TSFA Jex - - 2+2 z,zk - 4
 Course: Thermodynamics and Statistical Physics 02TSFA prof. Ing. Jex Igor DrSc. - 2+2 Z,ZK - 4 Abstract: Foundation of thermodynamics and statistical physics.Thermodynamic potential, the Joule Thomson effect, conditions of equilibrium, the Braun-Le Chatelier principle.Statistical entropy. Basics of many body description from a statistical point of view (classical and quasiclassical regime within the frame of a canonical and grand-canonical ensemble, Fermi gas, models of crystals and the black body radiation). The Boltzmann equation is used to discusses simple transport phenomena. Outline: 1.Statistical entropy, the most probable distribution 2.Statistical ensembles 3.Thermodynamic potentials 4.Equilibrium conditions 5.The phase rule, phase transitions 6.Thermodynamic inequalities, Braun-Le Chatelier principle 7.Statistical description and the thermodynamics of the ideal gas 8.Fermi-Dirac, Bose-Einstein statistics 9.Heat capacity of crystals 10.Black body radiation 11.Boltzmann?s transport equation 12.Boltzmann?s H-theorem, transport phenomena Outline (exercises): Solving exercises on the following topics 1.Statistical entropy, the most probable distribution 2.Statistical ensembles 3.Thermodynamic potentials 4.Equilibrium conditions 5.The phase rule, phase transitions 6.Thermodynamic inequalities, Braun-Le Chatelier principle 7.Statistical description and the thermodynamics of the ideal gas 8.Fermi-Dirac, Bose-Einstein statistics 9.Heat capacity of crystals 10.Black body radiation 11.Boltzmann transport equation 12.Boltzmann H-theorem, transport phenomena Goals: Knowledge: learn basic concepts of thermodynamics and statictical physics Skills: solve elementary problems of statistical physics and thermodynamics Requirements: mechanics, electricity and magnetism, theoretical physics Key words: Thermodynamics, equilibrium conditions, statistical entropy, statistical ensembles, transport equation References Key references: [1] Z. Maršák, Thermodynamics and statistical physics, ČVUT Praha, 1995 (in czech) Recommended references: [1] J. Kvasnica, Thermodynamics, SNTL Praha, 1965 (in czech) [2] J. Kvasnica, Statistical physics, Academia Praha 2003 (in czech) [3] H. B. Callen, Thermodynamics and an introduction to thermostatics, Wiley, New York, 1985

Theoretical Physics 102TEF12 Hlavatý, Jex, Tolar 2+2 z,zk 2+2 z,zk 4 4
 Course: Theoretical Physics 1 02TEF1 prof. RNDr. Hlavatý Ladislav DrSc. / prof. Ing. Jex Igor DrSc. / prof. Ing. Tolar Jiří DrSc. 2+2 Z,ZK - 4 - Abstract: The course is an introduction to methods of theretical physics (nonrelativistic, classical). The course communicates basic concepts of the Lagrange formalism and the efficiency of the method illustrated on elementary examples like the two body problem, elastic scattering and the motion of rigid bodies. Advanced parts of the course cover differential and integral principles of mechanics. The course is a preparation for the course TEF2. Outline: 1.Mathematical formalism 2.Newtonian mechanics 3.Lagrange function, constrains, generalised coordinates 4.Symmetries of the Lagrange function and conservation laws 5.Virial 6.Two body problem 7.Elastic scattering 8.Oscillations of coupled systems 9.Dynamics of rigid bodies 10.Classification of physical principles, the static equilibrium 11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz) 12.Integral principles (Hamilton, Jacobi, Maupertius) Outline (exercises): Solving exercises on the following topics: 1.Mathematical formalism 2.Newtonian mechanics 3.Lagrange function, constrains, generalised coordinates 4.Symmetries of the Lagrange function and conservation laws 5.Virial 6.Two body problem 7.Elastic scattering 8.Oscillations of coupled systems 9.Dynamics of rigid bodies 10.Classification of physical principles, the static equilibrium 11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz) 12.Integral principles (Hamilton, Jacobi, Maupertius) Goals: Knowledge: Learn the basics of analytical mechanics. The subject belongs to the course of physics at FNSPE. Skills: Application of methods of theoretical phzsics to solve concrete examples Requirements: 02MECH, 02ELMA Key words: Analytical mechanics, Lagrange formalism, Variational principles of mechanics References Key references: [1] I.Štoll, J. Tolar, Theoretical Physics, ČVUT 2002 (in Czech) Recommended references: [1] V. Trkal, Mechanics of Mass Points and Solid Bodies, ČSAV Praha 1956 (in Czech) [2] L.D. Landau, E.M. Lifšic, Teoreticeskaja fizika I, FIZMATGIZ Moskva, 2002 (in Russian)

 Course: Theoretical Physics 2 02TEF2 prof. RNDr. Hlavatý Ladislav DrSc. / prof. Ing. Jex Igor DrSc. / prof. Ing. Tolar Jiří DrSc. - 2+2 Z,ZK - 4 Abstract: The Hamilton formalism. The special theory of relativity: relativistic mechanics and classical field theory in the Minkowski space-time. Classical electrodynamics: Maxwell's equations in the Minkowski space - time, electromagnetic waves in dielectric media, electromagnetic radiation in the dipole approximation. Outline: 1. - 3. Hamilton's formalism 4. - 7. Special relativity 8. - 10.Electromagnetic field 11.-13. Electromagnetic waves. Electric dipole radiation Outline (exercises): Solving exercises on the following topics 1. - 3. Hamilton's formalism 4. - 7. Special relativity 8. - 10.Electromagnetic field 11.-13. Electromagnetic waves. Electric dipole radiation Goals: Knowledge: Learn the fundamentals of Hamilton's formalism, special relativity and electrodynamics. The subject belongs to the course of physics at FNSPE. Skills: Application of methods of theoretical phzsics to solve concrete examples. Requirements: 02TEF1 Key words: Hamiltonian, Hamilton's equations, conservation laws, canonical transformations, Hamilton-Jacobi equation, Minkowski spacetime, interval, Lorentz transformations, equations of motion for a relativistic particle, Maxwell's equations in a medium, potentials of electromagnetic field, Maxwell's equations in Minkowski spacetime References Key references: [1] I. Štoll, J. Tolar: Theoretical Physics (in Czech), ČVUT, Praha 2004 Recommended references: [2] J.D. Jackson: Classical Electrodynamics, Wiley, New York 1962 [3] H. Goldstein, C. Poole, J. Safko: Classical Mechanics, Addison-Wesley, New York 2002

Výuka jazyků04.. KJ - - - - - -
Introduction to Psychology00UPSY Lidická - - 0+2 z - 1
 Course: Introduction to Psychology 00UPSY PhDr. Oudová Drahomíra Ph.D. - - - - Abstract: Outline: Outline (exercises): Goals: Requirements: Key words: References

Introduction to Law00UPRA Čech - - 0+2 z - 1
 Course: Introduction to Law 00UPRA Mgr. Čech Martin - - - - Abstract: Outline: Outline (exercises): Goals: Requirements: Key words: References

Rhetoric00RET Kovářová - - 0+2 z - 1
 Course: Rhetoric 00RET Mgr. Kovářová Jana - - - - Abstract: The course is focused on the acquisition of speech and voice techniques and on the rules of correct pronounciation. The course is also devoted to the composition of public speech as well as to its nonverbal aspects. Stylistics exercises, strategies for coping with stage-fright and a short excursion into the history of rhetoric are an integral part of the course. Outline: 1. Introduction - rhetoric - purpose, history, outline of areas linked to rhetoric; - oral speech - purpose, listeners, environment; preparation for public speech 2. Language - "correct" form of written and spoken language; fillers; vocal and speech technique - intonation, volume, speed 3. Correct pronounciation; usage of foreign words, exercising of vocal organs 4. Composition of a speech - main points, introduction, conclusion; style a stylistics 5. Rhetorical techniques, tricks and tips; formulation; argumentation 6. Coping with stage-fright, relaxation and breathing; asertivity; empathy 7. Body language (facial expressions, gesticulation, posturology, proxemics), aesthetics of public appearance (politeness, etiquette, clothing etc.) 8. Analysis of real speeches; examples; rehearsing 9. Presentation tools and their usage, advantages and disadvantages; rules for PowerPoint presentation 10. Students´ presentations + analysis, feedback 11. Students´ presentations + analysis, feedback Outline (exercises): Goals: Knowledge: Familiarizing with the rules of contentual and formal preparation for a public speech. Skills: Acquisition of practical skills in this area and getting a feedback. Requirements: Key words: Rhetoric; body language; speaker metods References Key references: [1] ŠPAČKOVÁ, A.: Moderní rétorika. Praha: Grada Publishing 2009. Recommended references: [1] MAŘÍKOVÁ, M.: Rétorika. Manuál komunikačních dovedností. Praha: Professional Publishing 2000. [2] ŠMAJSOVÁ BUCHTOVÁ, B.: Rétorika. Vážnost mluveného slova. Praha: Grada Publishing 2010. [3] HIERHOLD, E.: Rétorika a prezentace. Praha: Grada Publishing 2005. [4] HOLASOVÁ, T.: Rétorika pro techniky. Praha: ČVUT 2004. [5] ŠESTÁK, Z.: Jak psát a přednášet o vědě. Praha: Academia 2000. [6] PLAMÍNEK, J.: Komunikace a prezentace. Praha: Grada Publishing 2008. [7] PLAMÍNEK J.: Řešení problémů a umění rozhodovat. Praha: Argo 1994. [8] HONZÁKOVÁ, M. - HONZÁK, F. - ROMPORTL, M.: Čteme je správně. Slovníček výslovnosti cizích jmen. Praha: Albatros 1996. [9] HŮRKOVÁ, J.: Česká výslovnostní norma. Praha: Scientia 1995. [10] CAPPONI, V. - NOVÁK, T.: Sám sobě mluvčím. Praha: Grada 1994. [11] TEGZE, O.: Neverbální komunikace. Praha: Computer Press 2003.

Economy in Technology00EKOT Fučíková - - 0+2 z - 1
 Course: Economy in Technology 00EKOT - - - - Abstract: The course introduces the basics of micro- and macroeconomics. Outline: 1. Introduction to economics. 2. Market, market mechanism and its elements. 3. Theory of consumer. 4. Production and cost functions in short and long terms. 5. Income, profit. 6. Firms in perfect competition. 7. Firms in imperfect competition. 8. Factors of production and respective markets. 9. Market failures and microeconomic policies. 10. Macroeconomic agregates. Total expenditure and product. 11. Money and money market. 12. Economic growth and economic cycle. 13. Unemployment. 14. Inflation. 15. Open economy, exchange rates, outer economic balance. 16. Monetary policy. 16. Government budget, fiscal policy. 17. International trade policy. Outline (exercises): Goals: Students should understand the market mechanism and market subjects' behavior in both, model and real situation, understand basic phenomena in economy, and ways that government can use to influence the economy. Requirements: Key words: microeconomics, macroeconomics, consumer, firm, perfect and imperfect competition, factors of production, product, money, economic growth, unemployment, inflation, exchange rate, external economic balance, economic policy References [1] Holman, R: Základy ekonomie - pro studenty vyšších odborných škol a neekonomických fakult VŠ, C.H. Beck, třetí vydání, 2015. [2] Liška, V., Sedláček, M.: Ekonomie pro techniky, Professional publishing, třetí vydání, 2010.

## Optional courses

Experimental Physics 202EXF2 Petráček 2+0 zk - - 2 -
 Course: Experimental Physics 2 02EXF2 doc. RNDr. Petráček Vojtěch CSc. 2+0 ZK - 2 - Abstract: Lecture represents an introductory course in experimental physics. Students will learn methods of measurement of basic physical quantities and methods of measurement evaluation. Outline: 1.Measurement of temperature 2.Calorimetry, thermal expansion 3.Usage of osciloscope 4.Basic electrotechnics 5.Analog instruments 6.Measurement of inner resistance 7.Compensation methods 8.Digital instruments, analog - digital conversion 9.Dosimetry of ionizing radiation 10.Detection of nuclear radiation 11.Principles and construction of particle detectors 12.Radioactivity 13.Excursion Outline (exercises): Goals: Knowledge: Basic experimental methods and routines in broad field of physics Abilities: Orientation in methods of experimental physics Requirements: Knowledge of basic course of physics Key words: Measurements of physical values, osciloscope, compensation methods, dosimetry, radiation, detection, radioactivity References Key references: [1] Brož: Fundamentals of Physical Measurement I., SNTL Praha 1983 (in Czech) Recommended references: [2] Kolektiv KF: Physical experiments I., ČVUT Praha 1989, (in Czech) [3] Kolektiv KF: Physics I - Laboratory experiments, ČVUT Praha 1998, (in Czech)

Experimental Laboratory 102PRA12 Bielčík 0+4 kz 0+4 kz 6 6
 Course: Experimental Laboratory 1 02PRA1 Mgr. Bielčík Jaroslav Ph.D. 0+4 KZ - 6 - Abstract: Lecture is intended especially for students who intend to study some of the physical specializations of FNSPE (branch Physical Engineering, Nuclear Engineering). But it can be also attended by students interested in the other specializations. In Experimental laboratory students learn how to prepare for experiments (including work with the literature), the implementation of the measurement (acquire of different experimental procedures and routines), will teach writing the records of measurement, processing and evaluation of results. At the same time practically extend the knowledge gained in lectures on physics. Outline: . Outline (exercises): 1.Cavendish experiment. 2.Elasticity, Hook´s law. 3.Air bench - The Law of Conservation of Energy, crashes. 4.Volume measurements, determination of the Poisson constant. 5.Gas thermometer, latent heat of water vaporization. 6.Surface tension, viscosity of air and oil. 7.Voltmeter, ammeter, compensator. 8. Sonar. 9.Basic acoustics experiments. 10.Driven harmonic oscillation, Pohl torsion pendulum. 11.Rotational dynamics, gyroscope. 12.Heat engine and heat efficiency. Goals: Knowledge: Experimental and analytic methods, different experimental procedures Abilities: Application of the mentioned methods on specific physical experiments, processing and evaluation of results Requirements: Knowledge of basic course of physics Key words: Experiments on mechanics, wave physics, electrics and magnetism References Key references: [1] Kolektiv KF: Physics I - Laporatory excersisies, ČVUT Praha 1998 (in Czech) Recommended references: [2] J.D.Wilson, C.A.Hernandez: Physics Laboratory Experiments, Brooks Cole Boston 2004 Media and tools: laboratory of the department of physics

 Course: Experimental Laboratory 2 02PRA2 Mgr. Bielčík Jaroslav Ph.D. - 0+4 KZ - 6 Abstract: Lecture is intended especially for students who intend to study some of the physical specializations of FNSPE (branch Physical Engineering, Nuclear Engineering). But it can be also attended by students interested in the other specializations. In Experimental laboratory students learn how to prepare for experiments (including work with the literature), the implementation of the measurement (acquire of different experimental procedures and routines), will teach writing the records of measurement, processing and evaluation of results. At the same time practically extend the knowledge gained in lectures on physics. Outline: Outline (exercises): 1.Capacity, electrostatic field. 2.Ferromagnetic hysteresis. 3.RLC circuits, driven and dumped oscillations. 4.Line spectra of Hg and Na spectral lamps using prism spectrometer. 5.Rtg spectrum of Mo anode. 6.Geometrical optics. 7.Microwawes. 8.Polarization of light. 9.Interference and diffraction of light. 10.Thermo-emission of electrons. 11.Specific electron charge, energy loss of alpha particles in gases. 12.Spectrum of gamma radiation. Goals: Knowledge: Advanced experimental and analytic methods and experimental procedures Abilities: Application of the mentioned methods on specific physical experiments, processing and evaluation of results Requirements: Knowledge of basic course of physics Key words: Experiments on wave physics, thermodynamics and nuclear physics References Key references: [1] Kolektiv KF: Physics I - Laporatory excersisies, ČVUT Praha 1998 (in Czech) Recommended references: [2] J.D.Wilson, C.A.Hernandez: Physics Laboratory Experiments, Brooks Cole Boston 2004 Media and tools: laboratory of the department of physics

Programming in C++ 118PRC12 Virius 4 z 4 kz 4 4
 Course: Programming in C++ 1 18PRC1 doc. Ing. Virius Miroslav CSc. 2+2 Z - 4 - Abstract: This course covers mainly the C programming language and non-object oriented features of the C++ language. Outline: 1.Introductory examples 2.Compilation, project 3.Basic constructs 4.Scalar data types in C and C++ 5.Expressions 6.Statements 7.Pointers, arrays and pointer arithmetics 8.Structs and unions 9.Functions 10.Preprocessor 11.Standard C library Outline (exercises): The sylabus of the excercises is the same as the sylabus of the lecture. Goals: Knowledge: The C programming language according to the ISO 9899:1990 and ISO 9899:1999 international standards and selected features of the C++ programming language. Ability: The student will be able to use this programming language to solve common programming tasks. Requirements: Basic programming skills (as covered by the "Basic of programming" course) Key words: C programming language;compilation;basic data type;lexical convention;array;pointer;pointer arithmetic;struct;union;statement;preprocessor;macro;C runtime library;memory management References Key references: [1] Virius, M: Programování v C++, 3. vyd. Praha, Vydavatelství ČVUT 2009. ISBN 978-80-01-04371-4 Recommended references: [1] Stroustrup, B.: The C++ Programming Language. 3rd edition. Addison-Wesley 1997. ISBN 0-201-88954-4. [2] Virius, M. Pasti a propasti jazyka C++. Druhé vydání. Brno, Computer Press 2005. ISBN 80-251-0509-1. [3] Eckel, B. Myslíme v jazyku C++. Praha, Grada Publishing 2000. ISBN 80-247-9009-2. 552 stran. (První díl) [4] Sutter, H. Exceptional C++. Addison-Wesley 2000. ISBN 0-201-61562-2. [5] Sutter, H. More Exceptional C++. Addison-Wesley 2002. ISBN 0-201-70434-X. [6] Koenig, A. C Traps and Pitfalls. Addison-Wesley 1989. ISBN 0-201-18928-8.

Practical Informatics for Technics 212PIN23 Šiňor 1+1 z 1+1 z 2 2
 Course: Practical Informatics for Technics 2 12PIN2 doc. Dr. Ing. Šiňor Milan 1+1 Z - 2 - Abstract: Practically oriented three semester course of basics and applications of informatics for science and engineering included as obligatory alternative course. Constituent part is realized in computer classrooms. The second part of the course is "Introduction to computer algebra systems?. Outline: Difficulties of scientific computing, algebraic and numerical computation, graphics. Computer algebra systems Maple, Mathematica and Maxima. Symbolic expressions, variables, functions and procedures. Simplification and manipulation with expressions, equations and systems of equations, fields and matrices. Symbolic derivative, integration, series, differential equations. Visualizations and animations. Elementals of programming in Maple and Mathematica. Outline (exercises): Difficulties of scientific computing, algebraic and numerical computation, graphics. Computer algebra systems Maple, Mathematica and Maxima. Symbolic expressions, variables, functions and procedures. Simplification and manipulation with expressions, equations and systems of equations, fields and matrices. Symbolic derivative, integration, series, differential equations. Visualizations and animations. Elementals of programming in Maple and Mathematica. Goals: Knowledge: The goal is to provide prospective engineers with such knowledges of computer technology and informatics that are at present necessary for effective practice of professional activities. Skills: Constituent part is realized in computer classrooms as practical exercises. This leads to acquirement of experience gained. Requirements: Key words: Algebraic and numerical computation. Computer algebra systems, Maple, Mathematica, Maxima. Symbolic manipulations, graphics. References Key references: [1] Maple 14 Full Manual Set, Maplesoft 2010. Recommended references: [2] S. Wolfram: The Mathematica Book, Fifth Edition. Wolfram Media 2003.

 Course: Practical Informatics for Technics 3 12PIN3 doc. Dr. Ing. Šiňor Milan - 1+1 Z - 2 Abstract: Practically oriented three semester course of basics and applications of informatics for science and engineering included as obligatory alternative course. Constituent part is realized in computer classrooms. The third part of the course is "Introduction to scientific computing?. Outline: Interpreted and compiled languages: Interpreted languages Matlab, Scilab and Python as instruments for scientific computing. Scalar data types, declaration, operators and expressions. Functions, arrays, libraries, compound data types. Basic terms and numerical algorithms: Number representation, range and number of significant digits, IEEE arithmetics, rounding error, interval arithmetics, error accumulation. Solution of non-linear equations, bisection method, Newton's method. Numerical integration, rectangular and trapezoid method. Basic solution of ordinary differential equations, Euler method and its modification. Scientific documents and computer presentations: Particularity of scientific documents, text processors for scientific documents, mathematical text and graphics. Resources for DTP, typography system TeX. PostScript language. Outline (exercises): Interpreted and compiled languages: Interpreted languages Matlab, Scilab and Python as instruments for scientific computing. Scalar data types, declaration, operators and expressions. Functions, arrays, libraries, compound data types. Basic terms and numerical algorithms: Number representation, range and number of significant digits, IEEE arithmetics, rounding error, interval arithmetics, error accumulation. Solution of non-linear equations, bisection method, Newton's method. Numerical integration, rectangular and trapezoid method. Basic solution of ordinary differential equations, Euler method and its modification. Scientific documents and computer presentations: Particularity of scientific documents, text processors for scientific documents, mathematical text and graphics. Resources for DTP, typography system TeX. PostScript language. Goals: Knowledge: The goal is to provide prospective engineers with such knowledges of computer technology and informatics that are at present necessary for effective practice of professional activities. Skills: Constituent part is realized in computer classrooms as practical exercises. This leads to acquirement of experience gained. Requirements: Key words: Interpreted and compiled languages for scientific computing. Basic terms and numerical algorithms. Typography system for TeX scientific documents. References Key references: [1] D. C. Hanselman, B. Littlefield: Mastering Matlab 7. Prentice Hall 2004. Recommended references: [2] L. Lamport: LaTeX: A Document Preparation System (2nd Edition). Addison-Wesley 1994.

Dosimetry Seminar 116SED12 Johnová 0+2 z 0+2 z 2 2
 Course: Dosimetry Seminar 1 16SED1 Ing. Johnová Kamila - - - - Abstract: Introductory lectures on physics and dosimetry of ionizing radiation followed by lectures about routine and research activities in the field. Outline: Outline (exercises): Goals: Requirements: Key words: References

 Course: Dosimetry Seminar 2 16SED2 Ing. Johnová Kamila - - - - Abstract: Presentation of graduates and students on research topics in the field of dosimetry and medical physics. Outline: Outline (exercises): Goals: Requirements: Key words: References

Seminar on Calculus B101SMB12 Krbálek 0+2 z 0+2 z 2 2
 Course: Seminar on Calculus B1 01SMB1 doc. Mgr. Krbálek Milan Ph.D. 0+2 Z - 2 - Abstract: The course is devoted to support the lectures of Calculus B3. Outline: Physical applications of theory of differential equation, general properties of metric, norm and pre-hilbert spaces, Hilbert spaces of functions. Outline (exercises): Physical applications of theory of differential equation, general properties of metric, norm and pre-hilbert spaces, Hilbert spaces of functions. Goals: Knowledge: Application of mathematical theory to the practical tasks. Skills: Individual analysis of practical exercises. Requirements: Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01LA1, 01LAB2 held at the FNSPE CTU in Prague). Key words: Solution of differential equations, metric spaces, normed and Hilbert?s spaces. References Key references: [1] Robert A. Adams, Calculus: A complete course, 1999, [2] Thomas Finney, Calculus and Analytic geometry, Addison Wesley, 1996 Recommended references: [3] John Lane Bell: A Primer of Infinitesimal Analysis, Cambridge University Press, 1998 Media and tools: MATLAB

 Course: Seminar on Calculus B2 01SMB2 doc. Mgr. Krbálek Milan Ph.D. - 0+2 Z - 2 Abstract: The course is devoted to support the lectures of Calculus B4. Outline: Regular mappings in two- or three-dimensional space, analytical forms of tangent hyperplanes to quadrics and pseudo-quadrics, volumes of chosen bodies, derivative of integral with parameter, application of measure theory and theory of Lebesgue integral. Outline (exercises): Regular mappings in two- or three-dimensional space, analytical forms of tangent hyperplanes to quadrics and pseudo-quadrics, volumes of chosen bodies, derivative of integral with parameter, application of measure theory and theory of Lebesgue integral. Goals: Knowledge: Application of mathematical theory to the practical tasks. Skills: Individual analysis of practical exercises. Requirements: Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01MAB3, 01LA1, 01LAB2 held at the FNSPE CTU in Prague). Key words: Function of several variables, measure theory, theory of Lebesgue integral References Key references: [1] M. Giaquinta, G. Modica, Mathematical analysis - an introduction to functions of several variables, Birkhauser, Boston, 2009 Recommended references: [2] S.L. Salas, E. Hille, G.J. Etger, Calculus (one and more variables), Wiley, 9th edition, 2002 Media and tools: MATLAB

Physical Training 100TV12 ČVUT - z - z 1 1
 Course: Physical Training 1 00TV1 - - - - Abstract: Outline: Outline (exercises): Goals: Requirements: Key words: References

 Course: Physical Training 2 00TV2 - - - - Abstract: Outline: Outline (exercises): Goals: Requirements: Key words: References