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Tento výpis sylabů a studijních plánů je založen na podkladech k Bílé knize a na jednorázovém exportu dat z KOSu podle staré akreditace z roku 2014. Nové obory s novými studijními plány zatím nejsou pro elektronický export připraveny a je otázka, zda se to do konce roku 2020 stihne. Obsah a osud této stránky je tak zatím nejistý.

# Curricula and Syllabi of FNSPE CTU in Prague

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## Aktualizace dat: 28.8.2019

Year 2
course code teacher ws ss ws cr. ss cr.

## Compulsory courses

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

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 Schmidt, 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. Introduction to quantum physics: black body radiation, quantum of energy, photoeffect, the Compton effect, the de Broglie waves, the Schrodinger equation, stationary states and spectra of finite systems. Outline: 1. Oscillations of systems of mass points 2. Travelling waves in non-dispersive media 3. Waves in dispersive media 4. Energy and reflection of waves 5. Electromagnetic waves 6. Polarization 7. Interference and diffraction 8. Geometrical optics 9. Black body radiation, photons 10. The de Broglie waves 11. The Schrodinger equation 12. Stationary states and spectra 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. Energy and reflection of waves 5. Electromagnetic waves 6. Polarization 7. Interference and diffraction 8. Geometrical optics 9. Black body radiation, photons 10. The de Broglie waves 11. The Schrodinger equation 12. Stationary states and spectra Goals: Knowledge: Physics of mechanical and electromagnetic oscillations and waves, introduction to quantum 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 a slit, Fermat's principle, the Kirchhoff and Planck laws of radiation, photoeffect, the de Broglie waves, the Schrodinger equation, stationary states and spectra 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 //physics.fjfi.cvut.cz [4] H. Georgi: The Physics of Waves, Prentice Hall, Upper Saddle River NJ 2015 (http://www.people.fas.harvard.edu/~hgeorgi/onenew.pdf)

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 Jex, Novotný 2+2 z,zk 2+2 z,zk 4 4
 Course: Theoretical Physics 1 02TEF1 prof. Ing. Jex Igor DrSc. 2+2 Z,ZK - 4 - Abstract: The course is an introduction to analytical mechanics. The students acquire knowledge of the basic concepts of the Lagrange formalism. The efficiency of this method is illustrated on elementary examples like the two-body problem, the motion of a system of constrained mass points, and of a rigid body. Advanced parts of the course cover differential and integral principles of mechanics. The subject is the first part of the course of classical theoretical physics (02TEF1, 02TEF2). Outline: 1. Mathematical formalism 2. Newtonian mechanics 3. The Lagrange function, constraints, generalised coordinates 4. Lagrange equations 5. Symmetries of the Lagrange function and conservation laws 6. Virial theorem 7. The two-body problem 8. Oscillations of systems of mass points 9. Dynamics of rigid bodies, Euler's equations 10. Static equilibrium, the principle of virtual displacements 11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz) 12 .Integral principles of Hamilton, Maupertuis and Jacobi Outline (exercises): Solving exercises on the following topics: 1.Mathematical formalism 2.Newtonian mechanics 3.Lagrange function, constraints, generalised coordinates 4. Lagrange equations 5.Symmetries of the Lagrange function and conservation laws 6.Virial theorem 7. The two-body problem 8. Oscillations of coupled systems 9 .Dynamics of rigid bodies, Euler's equations 10. Static equilibrium, the principle of virtual displacements 11. Differential principles (d´Alembert, Jourdain, Gauss, Hertz) 12. Integral principles of Hamilton, Maupertuis and Jacobi Goals: Knowledge: Learn the basics of analytical mechanics. The subject belongs to the course of classical theoretical physics at FNSPE. Skills: Application of methods of theoretical physics to solve concrete examples Requirements: 02MECH, 02ELMA Key words: Analytical mechanics, the Lagrange formalism, variational principles of mechanics References Key references: [1] I. Štoll, J. Tolar, I. Jex, Classical Theoretical Physics, Karolinum, Prague 2017 (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, Teoretičeskaja fizika I, FIZMATGIZ, Moskva 2002 (in Russian)

 Course: Theoretical Physics 2 02TEF2 Ing. Novotný Petr Ph.D. - 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. Hamilton's formalism 2. Special relativity 3. Electromagnetic field 4. Electromagnetic waves. Electric dipole radiation Outline (exercises): Solving exercises on the following topics 1. Hamilton's formalism 2. Special relativity 3. Electromagnetic field 4. Electromagnetic waves. Electric dipole radiation Goals: Knowledge: Learn the fundamentals of Hamilton's formalism, special relativity and classical electrodynamics. The subject represents the second part of the course of classical theoretical physics at FNSPE. Skills: Application of methods of theoretical phzsics to solve concrete examples. Requirements: 02TEF1 Key words: The hamiltonian, Hamilton's equations, conservation laws, canonical transformations, the Hamilton-Jacobi equation, the Minkowski spacetime, the interval, the Lorentz transformations, equations of motion for a relativistic particle, Maxwell's equations in a medium, potentials of the electromagnetic field, Maxwell's equations in the Minkowski spacetime, retarded potentials, electric dipole radiation References Key references: [1] I. Štoll, J. Tolar, I. Jex: Classical Theoretical Physics, Karolinum, Praha 2017 (in Czech) 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

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 principle programming language as a demonstration tool. The seminars are held in computer laboratory. 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, MATLAB system, ordinary differential equations. References Key references: [1] W.H. Press, B.P. Flannery, S.A. Teukolsky, V. H. Vetterling: Numerical Recipes in C++ (The art of scientific computing), Cambridge University Press, Cambridge, 3rd edition 2007 (also versions for C, 2nd edition 1993 and Fortran, 2nd edition 1993) (available at http://www.numerical.recipes/oldverswitcher.html). 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 Matlab program.

Introduction to Nuclear Reactor Physics 117ZAF1 Štefánik, Sklenka 3+1 kz - - 4 -
 Course: Introduction to Nuclear Reactor Physics 1 17ZAF1 Ing. Štefánik Milan Ph.D. 3+1 KZ - 4 - Abstract: The lectures start with a description of the microworld structure at the level of electrons, protons and neutrons. A description of radioactivity and nuclear reactions follows subsequently. Great focus is given to neutron interactions with matter. The probability of nuclear reactions is described by introducing of cross-sections in dependence on the neutron energy. Fission of heavy atoms is the important process for the operation of nuclear reactors. The students will get familiar with issue of nuclear chain reaction, energy released from fission reaction, and issue of neutron balance. Then the most important reactor types are described including the complete scheme of nuclear power plant with the light water reactor. The analysis of diffusion environments is based on the application of the diffusion equation obtained from Fick's law. Students will be able to determine the neutron flux distribution in various diffusion environments with the point source, planar source, and linear source. Outline: 1. Atom and nuclear physics 2 lectures Introduction to problems, goals of the lectures, fundamental particles, structure of atom and nucleus, nuclear force, quantities and units, excited states, radioactivity and radioactive decay, nuclear stability, kinetics of radioactive decay, decay series, binding energy, mass defect. 2. Interaction of neutron with matter 2 lectures Interactions of neutron with nucleus, neutron beam intensity, reaction rate and microscopic cross-section, neutron beam attenuation, neutron flux density, excitation functions - elastic scattering, inelastic scattering, cross-section of radiative capture, cross-section of fission, total cross-section; characteristics of neutron sources. 3. Neutron slowing down 3 lectures The energy loss in elastic collisions, neutron scattering on hydrogen, neutron lethargy, neutron energy spectrum - Maxwellian spectrum (energy and rate distribution), thermal neutrons, thermal neutron flux, one-group thermal cross-section; neutron moderation, the macroscopic slowing down power and the moderating ratio. 4. Nuclear fission 3 lectures Discovery of nuclear fission, fission process - liquid drop model of nucleus; fission reaction - critical energy of fission, fissile and fissionable nuclides; fission cross-section; fission products, neutron production, energy released in fission, spontaneous fission; nuclear chain reaction - multiplication factor, reactivity; neutron balance - infinite and finite system; four factor formula; prompt and delay neutrons; prompt neutron spectrum; fuel production and consumption. 5. Nuclear reactors 1 lecture Basic terminology, categorization of nuclear reactors, nuclear power plant - 1st loop, 2nd loop, and 3rd loop; types of nuclear reactors, fuel cycle - front end, service period, and back end. 6. Fick's law 1 lectures Neutron diffusion, neutron flux density and neutron current density, Fick's law - introducing of Fick's law, physical interpretation, verification of assumptions; transport cross-section, validity of Fick's law. 7. Diffusion theory 3 lectures The equation of continuity, diffusion equation - validity of diffusion equation and boundary conditions; mathematical apparatus - Bessel functions, modified Bessel functions; neutron flux distribution in infinite environment; diffusion length, neutron sources in infinite environment - point source, planar source, and linear source, diffusion parameters. Outline (exercises): 1. Atom physics and radioactivity 2 excercises Molar mass calculation, atomic ratio and mass fraction, atomic density calculation, radioactivity and production rate, Q-val. of nuclear reaction, binding energy, mass defect. 2. Interaction of neutron with matter 2 excercises Cross-section calculations (microscopic and macroscopic), reaction rate and neutron flux, attenuation of neutron beam intensity, neutron beam density, kinematics of collision processes, collision parameter, nuclear fission modes. 2. Neutron balance, fuel cycle 1,5 excercises Neutron balance calculation, multiplication factor, fuel production and consumption, one-group neutron flux density in nuclear reactor, calculation of multiplication factor and reproduction factor for thermal and fast reactors. 4. Diffusion theory 1,5 excercises Calculation of neutron flux distribution in diffusion environment, point source, planar source, and linear source, one-group thermal cross-section, diffusion length and diffusion coefficient, transport mean free path, application of boundary conditions. Goals: Knowledge: Students have good knowledge on properties and types of nuclear reactions, issues of cross-sections, nuclear fission and neutron balance. They have knowledge on the composition of the atom nucleus, the properties of the diffusion environment and the fissile and fissionable materials. Abilities: good overview in problems, application of obtained knowledge in other subjects in the field of reactor physics, ability to work with nuclear data, ability to determine the atomic densities of materials that are necessary for all analyzes performed in reactor physics and ability to perform calculation of neutron flux distribution in simple geometries using the diffusion equation. Requirements: Key words: Reactor physics, nucleus, neutron, cross-section, multiplication factor, reactivity, reproduction factor, thermal utilization factor, Fick's low, diffusion equation References Key references: 1. Lamarsh J. R.: Introduction to Nuclear Engineering, 3rd Ed., Prentice Hall, 2001 2. Frýbort J., Heraltová L., Štefánik M.: Úvod do reaktorové fyziky: teorie a cvičení. Skripta ČVUT v Praze, 2013, ISBN 978-80-01-05322-5 3. Zeman J.: Reaktorová fyzika 1, skripta ČVUT v Praze, 2003, ISBN 80-01-01933-0 Recommended references: 1. Heřmanský, B.: Jaderné reaktory. SNTL, Praha, 1981 2. DOE Fundamentals Handbooks - Nuclear Physics and Reactor Theory, Vol. 1 a Vol. 2, 1993, DOE-HDBK-1019/1-93 3. Reuss P.: Neutron Physics, EDP Sciences, 2008

Thermohydraulics Design of Nuclear Devices 117THNJ12 Kobylka, Heřmanský 2+0 z 2+1 z,zk 2 3
 Course: Thermohydraulics Design of Nuclear Devices 1 17THNJ1 Ing. Kobylka Dušan Ph.D. 2+0 Z - 2 - Abstract: With this course, students are introduced into the problem of thermal calculation and design of nuclear devices thermodynamic diagrams. Step by step they will learn more about basic quantities and terms in technical thermodynamic, basic reversible and non-reversible thermodynamic changes and cycles with ideal gas. The main focus of course is in thermodynamic of steam: basic reversible and non-reversible thermodynamic changes with steam and Rankine-Clausius cycle. In detail are analyed miscellaneous methods of thermal efficiency increasing of Rankine-Clausius cycle. Course closure is dedicated to thermodynamic of gas mixtures and humid air. Outline: 1. Introduction to course, terms and quantities definition Duration: 1 lecture Introduction to issue, references, course integration into study and relationship to other courses, students motivation, terms and quantities definition for field of technical thermodynamic (entropy, specific heat, enthalpy, etc.) 2. Thermodynamic laws, Thermodynamic diagrams Duration: 2 lectures The 1st thermodynamic law and its importance in power engineering, miscellaneous notations of the 1st thermodynamic law and their use for calculations, 2nd thermodynamic law and its importance for thermal machines design, working diagram, thermal diagram, h-s diagram, their importance and use, definition and calculation of work (pressure, volume, cycle). 3. Thermodynamic of ideal gas Duration: 3 lectures Definition and fundamental characteristic of ideal gas and their equation of state, basic reversible and non-reversible thermodynamic changes (isochoric, isobaric, isothermic, isoentropic and polytropic), gas expansion in turbine and compression in compressor (definitions, calculations of state quantities, heat and works), thermodynamic cycles: direct, reverse, cycle efficiency definition, Detailed description and calculations of cecles: Carnot, Brayton and cycles of combustion engines. 4. Thermodynamic of steam Duration: 6 lectures Introduction to thermodynamic of steam, steams and their equations of state, diagrams of water and steam: thermal, working and h-s, their description, construction and importance, definition of quantities and terms (moist steam, saturated steam, superheated steam, etc.), steam tables and their use. Basic reversible and non-reversible thermodynamic changes with steam (isochoric, isobaric, isothermic, isoentropic, steam mixing, etc.). Rankine-Clausius cycle with superheated and saturated steam (description, importance, calculations) and its thermal efficiency increasing (especially regeneration and reheating), calculations and optimalization of real Rankine-Clausius cycle. 5. Thermodynamic of mixtures and humid air Duration: 1 lecture Thermodynamic of mixtures (calculation of state quantities, equation of sate), humid air: definition, humidity, enthalpy, Molliér?s diagram, humid air importance in calculations. Outline (exercises): Goals: Knowledge: detailed knowledge of thermodynamic of ideal gas and especially thermodynamic of steam (basic changes and cycles). Deatiled knowledge of Rankin?Clausius cycle and methods of its thermal efficiency increasing and optimalization. Abilities: orientation in issue, apply gained knowledge in practice and in next parts of course THN (2 a 3) and courses which are focused on thermomechanic and design of devices in nuclear power plant as well as control of nuclear power plant. Requirements: Key words: technical thermodynamic, ideal gas, thermodynamic change, thermodynamic cycle, thermodynamic of steam, Carnot cycle, Brayton cycle, Rankine-Clausius cycle, regeneration, carnotization, reheating, humid air References Key references : 1. Kobylka, D.: Technická termodynamika s řešenými příklady, Česká technika - nakladatelství ČVUT, Praha 2016, ISBN 978-80-01-05902-9 2. Mareš R. - Šifner O. - Kadrnožka J.: Tabulky vlastností vody a vodní páry podle průmyslové formulace IAPWS-IF97, VUTIUM , 1999, ISBN 80-214-1316-6 Recommended references: 1. Kadrnožka, J.: Tepelné elektrárny a teplárny, SNTL, Praha, 1984 2. Sazima M., Kmoníček V., Schneller J., a kol.: Teplo, SNTL, Praha, 1989 3. Nožička J., Adamec J., Váradiová B.: Termomechanika - Sbírka příkladů, Vydavatelství ČVUT, Praha 2002 4. Sonntag E.R., Wylen G.J.V.: Introduction to Thermodynamics: Classical and Statisctical, John Wiley & sons, 1971, ISBN: 0-471-81365-6

 Course: Thermohydraulics Design of Nuclear Devices 2 17THNJ2 prof. Ing. Heřmanský Bedřich CSc. / Ing. Kobylka Dušan Ph.D. - 2+1 Z,ZK - 3 Abstract: With this course, students are introduced into problem of thermohydraulic calculations. Step by step they will learn more about fluid mechanics. The most important part dedicated to fundamentals: description of flow, definition of quantities and equations, pressure drops, 1D description of flow, turbulence and its influences on the flow characteristics, boundary layers and centrifugal pumps. That way students obtain knowledge which are necessary for insight into convection as well as into fundamental principles of devices in nuclear power plants. Outline: 1. Introduction to fluid mechanics, definition of terms and quantities Time range: 1 lecture Introduction to fluid mechanics, definition of basic quantities in fluid mechanics (pressure, velocity field, etc.), description of basic fluid properties (viscosity, surface tension, etc.), Newton?s law, fluid classification according to viscosity. 2. Fluid statics Time range: 2 lecture Hydrostatic pressure, Archimedes principle and floating, force caused on areas in fluid (plane, general), derivation of hydrostatic Euler?s equation and their use: fluids in relative equilibrium, equipotential surfaces. 3. Fluid kinematics Time range: 1 lecture Basic terms (flow line, vorticity, vortex line, velocity circulation, etc.) and laws (Helmholtz?s theorem, theorem of Stokes, etc.), derivation of mass conservation equation (equation of continuity), potential flow (definition), complex potential function and its use for calculation, flow around basic shapes. 4. Equations of fluid dynamics Time range: 2 lectures Basic definition in fluid dynamics, Euler?s equation of fluid dynamics, Navier-Stokes equations for uncompressible and compressible fluids (derivation, boundary conditions) calculation of basic types of flow, definition of hydraulic diameter. 5. Turbulent flow Time range: 1 lecture Definition of turbulent flow and its description according to Euler and Lagrange, methods of description and calculation of turbulent flow: Reynolds equations and their closure, Reynolds tensions, turbulent kinetic energy, basic features of turbulence, Boussinesque hypothesis, turbulent viscosity, influence of turbulence on flow characteristics. 6. 1D flow and pressure drops Time range: 3 lectures Derivation of Bernoulli's equation and Euler-Lagrange?s equation, use of equations for 1D flow calculations, loss energy, simplification of selected flows on 1D flow and their solving: outflows, shrouds, Prandtl and Pitott pipes, transient 1D flow, Definition of pressure drops, pressure drops on local losses ? coefficients of local losses: bends, valves and fittings, restrictions, etc., local losses in nuclear reactors (entrance, exit, spacer grids, ?), friction pressure losses, friction factor and its determination, acceleration pressure loses, televation pressure losses, calculations of pressure drops, use of pressure losses for calculation of velocity profile in circular pipe (power law). 7. Theorem about momentum flow change Time range: 1 lecture Derivation of theorem about momentum flow change, use of theorem about momentum flow change for calculations: action of force on channels, walls and curved areas, Pelton bucket, Pelton turbine, jet pumps. 8. Flow of real fluid around surfaces, boundary layer Time range: 1 lecture Definition, origin and types of boundary layer, basic features of boundary layer, description and solving of plane boundary layer, flow around curved walls and separation of boundary layer, calculation of forces. 9. Rotating channel centrifugal pumps Time range: 1 lecture Theory of rotating channel, equation of rotating channel, aplocation in vcentrifugasl pump, pumping equipment and specific pump energy, pump characteristics (Q-H characteristic), pump choice for piping. Outline (exercises): Selected chapters are demonstrated on simple examples (hydrostatic pressure, force caused on areas in fluid, Archimedes principle and floating, complex potential function, Navier-Stokess equation, pressure drops, Bernoulli's equation and Euler-Lagrange?s equation, Theorem about momentum flow change, pumping equipment, ...) Goals: Knowledge: students will get basic knowledge about field of fluid mechanics and heat transfer, which they can use especially in solving of thermohydraulic of primary circuit and nuclear reactors core. This basic knowledge will allow them to get in detail designs of another devices of the nuclear power plants (for example heat exchangers, steam generators, condensators, pumps, etc.) and they will allow them to understand their operational and physical features. Abilities: Students will be better orientated in the given problematics and they will be able to work on basic simplified designs. Obtained knowledge will use in the following parts of this course (17THN3) and all consecutive course, which are focused on thermal and hydraulics problematic or designing of single devices in nuclear power plant. On base of given knowledge students will be able to understand and analyse behavior and control of nuclear power plant as a complex. Requirements: THNJ1 Key words: fluid mechanics, hydrostatic, hydrodynamic, turbulent flow, pressure losses, pressure drops, Bernoulli's equation, Euler-Lagrange?s equation, boundary layer, pump characteristics, centrifugal pump, References Tong, L.S., Weisman, J.: Thermal Analysis of Pressurized Water Reactors, American Nuclear Society, Illinois USA, 1996, ISBN: 0-89448-038-3

Nuclear Reactors17JARE Heřmanský - - 2+0 zk - 2
 Course: Nuclear Reactors 17JARE Ing. Bílý Tomáš Ph.D. / prof. Ing. Heřmanský Bedřich CSc. - 2 ZK - 2 Abstract: Introduction. World power issue. Previous evolution of power reactor. Nuclear fission reactors, fuel assemblies, active core, control systems, safety systems, containment. Classification of reactors into IV generations. Standard types of nuclear power reactors: concept, description, layout, previous evolution, world share, perspectives. Pressurized water reactors (PWR). Western-type PWR (Westinghouse, KWU, Framatom). VVER-type reactors , Temelín nuclear power plant. Boiling water reactors. Heavy water reactors, fast breeder reactors, high-temperature gas cooled reactors. Second nuclear era. reactors of generation III (EPR, AP-1000, VVER 1200). Reactors of generation IV: GIF and INPRO initiatives. Evaluation and selection of proposed systems. Six selected concepts. ICRP scenarios of word evolution, hydrogen power, role of nuclear power in long-term outlook Outline: 1. Introduction Scope: 1 lecture Role of the course within study-program, relationship to other courses, goals of the course. Power issue, short-term approach, mid-term outlook, long-term perspectives. Nuclear power in the world. 1st and 2nd nuclear era. Nuclear power reactor and its parts: fuel assemblies, active core, reactor control systems, nuclear power plant, heat removal system, safety systems, containments. 2. Standard types of nuclear power reactors Scope: 1 lecture Evolution of nuclear power reactors - 1st nuclear era. Nuclear power in the world, NPP in operation, NPP under construction, planed and proposed reactors. NPP in permanent shut-down. Nuclear power and a EU. Is nuclear power really in depression? 3. Nuclear reactors of generation II. Scope: 6 lectures Pressurized water reactors (PWR) Previous evolution of pressurized water reactors. Basic concept of PWR. Layout of NPP with PWR reactor: active core and fuel assemblies, reactor vessel, control rod drivers, primary loop, safety systems-mechanical and technological part, Containments of NPP with PWR. Western type pressurized water reactors World share. Westinghouse-type pressurized water reactors, containment. Combustion Engineering type PWR. PWR design of ABB+CE company: systém 80+. KWU pressurized water reactors, Convoy project. FRAMATOM pressurized water reactors. NPP with VVER-type pressurized water reactor 1st phase of VVER reactors evolution. Specialties of VVER reactors evolution. VVER-440 type reactors of the first generation (V-230). VVER-440 type reactors of the second generation (V-213). VVER-440 type reactors of V1 NPP, barbotage condenser system. Containment with ice condenser (NPP Loviisa). Final remarks to VVER-440 unit. VVER -1000 type reactors Evolution of NPP with VVER-1000 type reactors. NPP concept and reactor layout: fuel assembly, control assembly, reactor internals, reactor vessel, reactor, primary loop and containment. Evolutionary trends of VVER-type reactors. Comparison of VVER-type and western PWR reactors, differences in active core, primary loop and safety systems. Other reactors of generation II: BWR,HWR, FBR Boiling water reactors (BWR): basic concept of BWR, General Electric BWR, Swedish BWR, advanced boiling water reactor (ABWR). Heavy water reactors (HWR): previous evolution of HWR, Canadian HWR, CANDU-950, Czechoslovak heavy water reactor KS 150. Fast breeder reactors (FBR): early evolution, basic concept, fuel assemblies, safety, French fast reactor Super Phenix. Other reactors of generation II: High temperature reactors HTGR Basic concept, layout, construction. Fuel: microparticles, hexagonal and spherical fuel assemblies. Active core. Safety of high-temperature reactors. NPP Fort St. Vrain and THTR-300. Modular HTGR concept. Safety of modular HTGR. New focus on HTGR: SA PBMR. 4. Nuclear reactors of generation III Scope: 3 lectures Topics: Requirements on generation III nuclear power reactors. Requirements of European users on NPP with light-water reactors (EUR): safety, economics, reliability, Pu recycling, plant lifetime extension. Selection of new nuclear source for mid-term outlook: six recommended systems (ABWR, AP-1000, ESBWR, GT-MHR, PBMR, SWR-1000) European pressurized water reactor (EPR) design Globalization of NPP producers. EPR design: organization, history and present state. Basic description of EPR, plant layout, containment and core catcher. EP/AP 1000 reactor of Westinghouse company: design evolution, reactor concept, reactor safety and safety functions. New designs of NPP with VVER type reactors of generation III Basic description of the designs. JE-91/99, JE VVER-1000 Type V-392 (JE-92), JE VVER-2006 designs. Safety functions and safety systems. Emergency core cooling systems. Heat removal systém via secondary loop. Containment and core catcher. 5. Nuclear reactors of generation IV Scope: 1 lecture Topics: GIF and INPRO initiatives. Evaluation and selection of proposed systems. Six selected concepts (GFR, LFR, MSR, SFR, SGWR a VHTR). Perspectives for 21st century: ICRP world evolution scenarios, hydrogen power and the role of nuclear power in long-term outlook. Outline (exercises): - Goals: Knowledge: Survey of world, European, and Czech nuclear power. Orientation in various reactor types - advantages, disadvantages, current status, outlook. Detailed knowledge of pressurized water reactor concept and structure of NPPs Dukovany and Temelin. Abilities: Orientation in given issues, use of gained knowledge in other courses (Reactor Thermomechanics, Reactor Dynamics, Safety of Nuclear power plants), notion of new nuclear source build issues Requirements: 17ZAF Key words: power issue, nuclear reactors, fuel assemblies , active core, control systems, safety systems, containment, gen. III reactors, gen. IV reactors, pressurized water reactors, VVER, EPR, AP-1000, VVER 1200 reactors, boiling water reactors, heavy water reactors, fast breeder reactors, high temperature reactors, initiatives GIF, INPRO, ICRP, hydrogen power, hydrogen economy References Key references: Heřmanský B.: "Nuclear reactors I. a II.", ČVUT, Prague 2010 (in Czech) Recommended references: Weinberg, A.M., Spiewak, I., Barkenbus, J.N.: "The Second Nuclear Era".Oak Ridge As. Universities, 1984 Ingemarsson, K.F.: "European Utility Requirement - ten years on". Nuclear Europe Worldscan, Summer 2002 Edition. "Generation IV Roadmap Technology Goals for Generation IV Nuclear Energy Systems". US DOE NERAC, GIF-019, December 2002 "International Conference on Innovative Technologies for Nuclear Fuel Cycles and Nuclear Power (INPRO)" 23-26 June 2003, Vienna

Materials Science14NMA Haušild 2+1 kz - - 3 -
 Course: Materials Science 14NMA prof. Dr. Ing. Haušild Petr - - - - Abstract: Introduction to the Materials Science Outline: 1. Thermodynamics of metals and alloys, solidification of metals and alloys 2. Phase diagrams 3. Crystal structure, crystal lattice defects 4. Diffusion 5. Plastic deformation hardening 6. Recovery and recrystallization 7. Solid state transforms, precipitation, martensitic transformation 8. Fe-C phase diagram, thermomechanical treatment of steel 9. Non-ferrous metals and alloys 10. Deformation and fracture of metals and alloys 11. Non-metallic materials - ceramics 12. Non-metallic materials - polymers 13. Corrosion 14. Mechanical testing Outline (exercises): Phase transforms Gibbs phase rule Phase diagrams Miller indices Crystal lattice packing Stress, strain Goals: Knowledge: Acquire basic information about materials Skills: Orientation in material topics Requirements: - Key words: Materials science, phase transforms, crystal structure, mechanical properties, non-metallic materials, corrosion References Key references: [1] Donald R. Askeland, The science and engineering of materials, 2006. Recommended references: [1] Michael F. Ashby, D R H Jones, Engineering Materials 1: An Introduction to Properties, Applications and Design, 1998.

Excursion17EXK Kobylka - - 1 týden z - 1
 Course: Excursion 17EXK Ing. Kobylka Dušan Ph.D. - 1t Z - 1 Abstract: This course - excursion - has to provide the basic ideas about various nuclear devices of various parts of fuel cycle, their production and operations. There are several research centers, nuclear facilities, machine works, etc., that students visit during one week of their examination period. The works we visit usually are: NRI - Řež, plc., (reactors LR-0 a LVR-15), Škoda JS plc.. (reactor hall, test loop of control drive mechanism, production of control drive mechanism), radioactive wastes storage Richard, uranium mining (Dolní Rožínka or Mine of chemical mining in Stráž pod Ralskem ), Nuclear power plant Temelín, etc. Outline: - Outline (exercises): - Goals: knowledge of various types of nuclear devices and find idea about their operation Requirements: Only for students of study area TTJR a JZ Key words: nuclear power plant, nuclear reactor References -

Výuka jazyků04.. KJ - - - - - -

## Optional courses

Equipment Complex of Nuclear Power Plants 117TCJ1 Bouček, Kropík 2+1 z,zk - - 3 -
 Course: Equipment Complex of Nuclear Power Plants 1 17TCJ1 doc. Ing. Kropík Martin CSc. 2+1 Z,ZK - 3 - Abstract: Lectures are composed as encyclopedic overview of power current electrotechnical facilities using LV, HV and VHV and are focused on their utilization in nuclear power plants including power extraction to electrical network. Theoretical background is supported by examples from work experience along with parameters of currently used facilities used in power engineering with focus on NPPs. First, the general relations of the electric circuits theory and electromagnetic and electric field theories are recapitulated. Then the overview of electrotechnic materials (electric current conductors, semiconductors, magnetic flux conductors, insulators, dielectrics), their properties, applications. After general introduction, there follow lectures on particular types of electrical machines and devices, their characteristics, equivalent diagrams, phasor diagrams, applications in NPPs. Finally, electric facilities of NPPs are presented including most applied power extraction schemes and schemes for assuring unit auxiliaries and for common plant operations. Examples of electric schemes of Czech NPPs are given including electric devices parameters. Lectures are supported by technical visits of university labs (university power plant, high-voltage lab, electric machines lab). In the university power plant, the measurement on power unit model is carried out. This includes examples and evaluations of transients of artificially generated failure states. Outline: 1. Basic terms and relations of electrical circuits theory and theories of electromagnetic and electric fields. Maxwell equations. 2. Electrotechnic materials - insulators, dielectrics, their properties and applications, electric resistance testing, dissipation factor, resistor materials 3. Electrotechnic materials - conductors, magnetic flux conductors, semiconductors, superconductors, conductors for specific applications (carbons, copper alloys, contact materials), magnetization characteristics, dissipation reduction in magnetic circuits) 4. Electrical machines - classification, definition of characteristics, characteristics of machines and their loads, warming and its relation to the way of machine load, efficiency, electrodynamic forces 5. Non-rotating electric machines - transformers, classifications, principle, design, hour angle, characteristics, operational states, determination of parameters for equivalent diagram, phase diagrams, limiting and filtration properties 6. Non-rotating electric machines - specialized transformers, suppressors, chocking coils, machines' transformers, their specifics, accuracy, overcurrent number, desired purpose-dependent characteristics 7. Rotating electric machines - synchronous machines, principle, design, winding, cooling, rotors for turboalternators and salient pole alternators, attenuator function, rotor power supply, excitors, equivalent diagram, phase diagram 8. Rotating electric machines - synchronic machines, alternators, particular reactances and their influence on current transient during short-cuts, operational characteristics, static and dynamic stability, synchronizing, swinging, operation to transmission grid, solitary operation, synchronic engines and compensators 9. Rotating electric machines - asynchronous machines, principle, design, winding, start up and the means of starting currents decreasing, torque characteristics, equivalent diagram, cyclic diagram, phase diagram, asynchronous generators, single-phase asynchronous motors 10. Rotating electric machines - DC machines, applications, principle, design, winding, characteristics. Commutator motors, application, principle, design, winding characteristics. Stepper motors, applications, principle, design. Specialized motors, pumps for liquid metals. 11. Electrical facilities - switches for LV, HV and VHV, requirements on switching capabilities for particular switch types, design, placing into electrical diagram, methods of arc extinction 12. Fuse and protective electrical devices - fuses, circuit breakers, power protection, surge protection. Design, purpose, characteristics, and their placing into electrical diagram, selective protection, limiting capabilities, testing 13. NPP electrical equipment - requirements, power extraction scheme, unit auxiliaries' scheme and scheme of power-consumption for all operational and emergency states. Examples of NPP electrical schemes, including electrical equipment parameters. 14. Measurement on the physical model of power unit in university power plant: Alternator synchronizing with hard grid with evaluation of particular synchronization errors consequences. Magnetization impulse during transformer startup and its dependence on switching instant. Course of short circuit current in synchronous alternator. Emergency field weakening of the alternator and dependence of the transient on failure mode and shunt resistant size. Outline (exercises): Laboratory exercise takes place in university lab in the last week of classes. It is focused on measurement on power unit model with examples and evaluation of transients at operational and artificially generated failure states (transformer startup pulses, imprecise synchronizing, synchronous alternator shortcut, alternator field weakening at various failure modes. Calculation of practical values is incorporated into lectures. Goals: Knowledge: general overview of electrical power facilities used in NPPs, understanding of their principle, requirements on them in relation to other technologies, redundancy and diversity in assuring auxiliaries power supply in operational and emergency states of the unit to assure safe solution of particular situations Abilities: orientation in the field, ability to incorporate the obtained knowledge in context with knowledge of other NPPs technologies Requirements: Key words: Transformer, synchronous alternator, asynchronous motor, DC motor, electrical equipment, switcher, nuclear power plant, auxiliary power consumption, assured power supply References 1. Elektrické stroje, skripta ČVUT FEL 2000. 2. Zařízení jaderných elektráren, skripta ČVUT FJFI 1985. 3. Elektrické stroje, skripta ČVUT FEL 2000.

Operational States of Nuclear Reactors17PSJR Huml, Sklenka - - 2+1 kz - 4

Introduction in Nuclear Fuel Cycle17UPC Sklenka, Starý - - 2+0 kz - 2

Radioactive Waste Management17RAO Konopásková - - 2+0 zk - 2

Nuclear Legislation17ALE Bílková, Fuchsová - - 2+0 z - 2

Introduction to the Design of Nuclear Facilities17PROJ Bouda 2+1 z - - 3 -

Mathematics 301MAT34 Dvořáková, Krejčiřík, Tušek 2+2 z,zk 2+2 z,zk 4 4
 Course: Mathematics 3 01MAT3 doc. Mgr. Krejčiřík David DSc. 2+2 Z,ZK - 4 - Abstract: The subject summarises the most important notions and theorems related to the study of finite-dimensional vector spaces. Outline: 1. Vector spaces; 2. Linear span and independence; 3. Basis and dimension; 4. Linear transformations; 5. Operator equations; 6. Scalar product and orthogonality; 7. Linear functionals and adjoint; 8. Matrices; 9. Determinants; 10. Spectrum; 11. Matrix exponential; 12. Quadratic forms. Outline (exercises): 0. Complex numbers; 1. Examples of vector spaces and subspaces; 2. Linear dependence of vectors - problem with parametres. 3. Selection of basis vectors from a set of generators, completing a basis; 4. Injectivity and kernel of a linear mapping; 5. Examples of scalar products and orthogonalization process; 6. Examples of linear functionals and construction of adjoint mappings; 7. Operations with matrices and construction of the matrix of a linear mapping; 8. Working with determinants, computation of the inverse matrix; 9. Eigenvalues and eigenfunctions of matrices; 10. Construction of matrix exponential; 11. Properties of quadratic forms. Goals: Knowledge: Learning basic concepts of linear algebra necessary for a proper understanding of related subjects, such as analysis of functions of several variables, numerical mathematics, and so on. Skills: Applications of theoretical concepts and theorems in continuing subjects. Requirements: Basic high school mathematics. Key words: Vector space, subspace, linear dependence, basis, dimension, linear transformations, matrices, trace, determinant, orthogonality, spectrum, eigenvalues, eigenvectors, quadratic form, matrix exponential. References Key references: [1] S. Axler: Linear algebra done right, Springer, New York 2014 Recommended references: [2] J. Kopáček, Matematika pro fyziky II, UK, Praha, 1989. [3] Lecture notes on the hompeage of the lecturer.

 Course: Mathematics 4 01MAT4 Ing. Tušek Matěj Ph.D. - 2+2 Z,ZK - 4 Abstract: Linear and non-linear differential equations of the first order. Linear differential equations of higher order with constant coefficients. Multivariable calculus and its applications. Outline: 1. Linear differential equations of the first order 2. Non-linear differential equation of the first order 3. Exact and homogeneous equations. 4. Linear differential equations of higher order 5. Linear differential equation with constant coefficients 6. Quadratic forms 7. Limit and continuity of multivariable functions 8. Multivariable calculus 9. Total differential 10. Implicit function 11. Change of variables 12. Extreme values of multivariable functions 13. Multidimensional Riemann integral 14. Fubini theorem and substitution theorem. Outline (exercises): 1. Linear differential equations of the first order 2. Non-linear differential equation of the first order 3. Linear differential equations of higher order 4. Linear differential equation with constant coefficients 5. Limit and continuity of multivariable functions 6. Implicit function 7. Extreme values of multivariable functions 8. Multidimensional Riemann integral 9. Fubini theorem and substitution theorem. Goals: Knowledge: To learn how to solve some elementary classes of differential equations, especially LDE. To become familiar with multivariable calculus. Abilities: To apply the knowledge above to particular problems in engineering. Requirements: Basis course in single variable calculus and linear algebra (in the extent of the courses at FNSPE, CTU in Prague: 01MAT1, 01MAT2, 01MAT3). Key words: Differential equations, multivariable calculus. References key references: [1] J. Marsden, A. Weinstein: Calculus III, Springer, 1985. recommneded references: [2] W. Rudin: Principles of Mathematical Analysis, McGraw-Hill, 1976. [3] J. Stewart: Multivariable Calculus, 8th Edition, Brooks Cole, 2015.

Experiment Design and Control17NRE Kropík 2+1 z,zk - - 3 -
 Course: Experiment Design and Control 17NRE doc. Ing. Kropík Martin CSc. 2+1 Z,ZK - 3 - Abstract: Lecture deals with design and operation of systems for control of experiments, acquisition and evaluation of experimental data. It provides information about interfaces of personal computers for control of experimental systems (COM, USB, Firewire, LAN, GPIB), further about measuring systems with VME, VXI and LXI interfaces, discuss their advantages and disadvantages. Next, lectures deal with programming of measuring systems - special dedicated software, problems of use of high programming languages and especially use of graphical oriented development tools (Agilent VEE and LabView); data acquisition and evaluation. Finally, students prepare individual software project for data acquisition and evaluation. Outline: 1. Standalone equipment, PC cards for measurement and bus based measuring systems (VME, VXI, LXI). Examples or measuring instruments, their features and capabilities of computer control 2. Interfaces COM, USB, LAN a Firewire for communication among PC and instruments, examples and demonstration 3. GPIB (IEEE488.2) interface, systems based on VXI bus with practical demonstration 4. Basic software for control of measuring instruments, control of instruments by standard communication programs. 5. Graphical oriented development tool Agilent VEE 1; basics of developing environment, programming in VEE, interface for inputs and outputs 6. Graphical oriented development tool Agilent VEE 2; control of instruments, I/O drivers, work with files 7. Graphical oriented development tool Agilent VEE 3; work with variables, extended function for evaluation of experimental data, hierarchical structure of programs 8. Graphical oriented development tool LabView 1; basics of developing environment National Instruments LabView, software production in LabView, differences in comparison to Agilent VEE 9. Graphical oriented development tool LabView 1, control of instruments, data acquisition and evaluation 10. Demonstration of system for validation of software for VR 1 training reactor safety and control system controlled by software on basis of Agilent VEE 11. 13. Individual students work on given software project under lecturer's guidance Outline (exercises): Students gradually train work with measuring instruments, development tools for software, and finally, they develop individual software project for control of experiment, data acquisition and evaluation Goals: Knowledge: basic knowledge of systems for control of experiments, measurement of electrical values and data acquisition; programming in graphical oriented development systems intended for control of experiments Abilities: orientation in matter of computer control of experiments, ability practically use gained knowledge in own experimental work Requirements: 17ZEL Key words: graphical oriented development tools Agilent VEE and LabView, data acquisition and evaluation, interface, systems with USB, GPIB, LAN and VXI busses References Key references (aspoň 1 položka) Agilent VEE Pro User's Guide, Agilent Technologies, 2005 Getting Started with LabVIEW, National Instruments, 2009 Recommended references: Robert Helsel: Visual Programming with HP VEE, Prentice Hall, 1997 Hewlett Packard/Agilent Instruments Documentation

Alternative Energy Resources17AEZ Škorpil - - 1 týden z - 3
 Course: Alternative Energy Resources 17AEZ doc. Ing. Kropík Martin CSc. / prof. Ing. Škorpil Jan CSc. - 1t Z - 3 Abstract: This course allows students to get an overview of the problematic and basic information about sources and techniques of energy production. The main attention is focused on the principles of energy transformations, energy technologies and systems. The students will be able to qualify the power sources features: usual thermal power plants, nuclear power plants, steam-gas cycles, geothermal, water and wind power, biomass, thermal pumps, solar power, fuel rods and sea power. In this course, there are also included several measurements realized during one week intensive course, which will be focused on the problematic mentioned above. Outline: 1. Introduction, energy sources and possibilities if their use, classification and new trends 2. Fossil-fuel power plants and heating power plants, general principles, combustion, boilers 3. Fossil-fuel power plants and heating power plants, gas-steam cycle 4. Geothermal energy and energy of sea 5. Energy of water, principles, basic calculations, types of turbines, small hydroelectric plants 6. Wind energy, principles, types of wind turbines, wind power plant 7. Energy of biomass, types of use, biogas, combustion, pyrolysis 8. Heat pumps, principle, heat sources 9. Solar energy, theoretical backgrounds, solar heat technology, solar collectors 10. Solar energy, photovoltaic devices 11. Fuel cells, principles, fuel, history, technology 12. Fuel cells, technology of membranes, real aplications 13. Excursion Outline (exercises): - measurement of photovoltaic device efficiency; - measurement of solar collectors efficiency; - measurement of heat pump performance factor; - measurement of school wind power plant. Goals: Knowledge: basic knowledge of energy sources and energy production, principles of energy transformations and technology. Abilities: review of energy sources features Requirements: - Key words: Solar energy, water energy, wind energy, heat pump, geothermal energy, biogas, biomass. References Key references: Dvořák, L. Sources and energy transformations, textbook, ČVUT Praha, 1992, (In Czech) Recommended references: Beranovský, Jiří; Truxa, Jan: Alternative energz fo your house, EkoWATT, Brno, 2003. ISBN 80-86517-59-4 Media and tools: photovoltaic device, solar collectors, heat pump, school wind power plant

Experimental Physics 202EXF2 Chaloupka, Petráček 2+0 zk - - 2 -
 Course: Experimental Physics 2 02EXF2 RNDr. Chaloupka Petr Ph.D. / 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.

Basics of Experimantal Data Processing16ZEDB Pilařová 2+0 zk - - 2 -
 Course: Basics of Experimantal Data Processing 16ZEDB Ing. Pilařová Kateřina Ph.D. 2+0 ZK - 2 - Abstract: Statistical analysis of experimental data; univariate data; calibration; regression; multivariate data. Outline: 1. Introduction 2. Charakteristics of statistical distributions (univariate data) 3. Exploratory data analysis 4. Testing of hypothesis 5. Analysis of variance (ANOVA) 6. Correlation analysis 7. Linear regression analysis 8. Principal of nonlinear regression analysis 9. Calibration 10. Interpolation and approximation 11. Basic of statistical analysis of multivariate data - enters data 12. Statistical analysis of multivariate data - test of characteristics 13. Multivariate statistical analysis - methods of latent variables 14. Multivariate statistical analysis - classification methods Outline (exercises): . Goals: Knowledge: Orientation in application of statistical methods in experimental data processing. Abilities: Independent treatment of experimental data. Requirements: . Key words: treatment, experimental data, data analysis, statistics References Key references: [1] M.Meloun, J.Militky, Statistical analysis of experimental data, ACADEMIA Prague 2004 (in Czech) Recommended references: [2] M.Meloun, J.Militky, M.Hill, Computer analysis of multivariant data in examples, ACADEMIA Prague 2005 (in Czech)

Introduction to Ecology16ZIVB Čechák, Thinová 2+0 kz - - 2 -
 Course: Introduction to Ecology 16ZIVB prof. Ing. Čechák Tomáš CSc. / RNDr. Thinová Lenka Ph.D. 2+0 KZ - 2 - Abstract: The subject inform about basic of the ecologic principles, terms and ideas. It covers overview information regarding to particular components of the environment and evaluate economic indicators and sustainable development. Outline: 1. Introduction: human society and environment, definition and base terms in environment 2. Introduction to geology of the Earth 3. Global tectonic 4. Hydrosphere : water cycle 5. Basic elements in environment cycles 6. Food - proteins sources, energy sources, food cycles 7. Introduction to soil science 8. Introduction to biology 9. Waste (distribution, classification), waste dumping 10.Sources of energy in the human life 11. Alternative sources 12. Influence of the energy production on the environment 13. Principle of sustainable development 14. Excursion Outline (exercises): Goals: Knowledge: Unprecedented knowledge from the field of ecology and others natural sciences. Skills: Formation of the new ways of thinking focused to environment. Requirements: Key words: environment; atmosphere; hydrosphere; litosphere; biosphere; legislation and most important laws; sources and consequences of damage or the environment; remedials; renewable and no renewable sources; long-time maintenance of the landscape; life quality References Key references: [1] Artiola, J.E.: Environmental Monitoring and Characterization. Elsevier Academic Press, 2004. [2] Begon M., Harper J.L., Townsend C.R.: Ecology.3.edition. Blackwell Sci.Publ.1065 pp., 1996. [3] Pivnička K.: Ecology. SPN:204 pp., 1984. (in Czech) [4] Kachlík, V.(1996): Essentials of geology. UK Praha, 2008. (in Czech) [5] Braniš, M.: Introduction to ecology and environmental sciences. 2. edition. Informatorium Praha, 169 pp., 1999.(in Czech) [6] Braniš, M. et al.: Explanatory dictionary of selected nomenclature from the environmental sciences. Karolinum Praha. 46 pp., 1999.(in Czech) [7] Begon, M., Harper, J.L., Townsend, C.R.: Ecology - individuals, populations and communities.University Palackého press, Olomouc. 949 pp.,1990. (czech translation -in Czech) Recommended references: [8] Sternheim, M. M., Kane, J. W.: General Physics, John Wiley & Sons, New York 1991. [9] Sears,F. W., Zemansky, M. W.: University Physics, Addison-Wesley, New York 1991. [10] Storch, J. D., Mihulka, S. : Introduction to present-day ecology. Portál, Praha, 2000. (in Czech) [11] Dykyjová, D.: Methods of ecosystems studies. Akademia Praha. 692 pp, 1998. (in czech) [12] Matějka, V.: Ecology. University of environment, Prague, 1993. (in Czech) [13] Heřmanský, B., Štoll, I.: Energy for 21. century. (in Czech)

Fundamentals of Ionizing-Radiation Metrology16MEZB Čechák, Novotný P. 2+1 z,zk - - 4 -
 Course: Fundamentals of Ionizing-Radiation Metrology 16MEZB prof. Ing. Čechák Tomáš CSc. / Ing. Novotný Pavel 2+1 Z,ZK - 4 - Abstract: The course summarizes the basic objectives and content of ionizing radiation metrology. It deals with the interpretation of radiation quantities and units in metrology. It summarizes the theoretical and experimental foundations of metrology, the determination of basic parameters of radiation. Lectures are supplemented with basic summary of relevant legislation and regulations. Outline: 1. General metrology. 2. Legal metrology, units, metrology law. 3. Metrology in the Czech Republic. 4. Standardization of the activity, proportional detector, Townsend process. 5. Liquid scintillator, coincidence method. 6. Preparation of the sources. 7. Standardization of the neutron sources, Mn- bath. 8. Secondary standardization of the activity, radionuclide calibrators. 9. Data evaluation, uncertainty A and B. 10. Calorimeter as absolute method for doze, kerma and exposition measurement. 11. Standardization of the exposition and kerma, air-free chamber, cavity chamber. 12. Photon beams for secondary standardization, X-ray spectra, structure of the laboratory. 13. Measurement of the ionization current. Outline (exercises): 1. Data processing, uncertainty of type A, B, notions sample mean, sample standard deviation, activity determination. 2. Absolute method of measuring dose kerma and exposure, air-free chamber. 3. Books for secondary metrology, X-ray, gamma ray spectra description, implementation, organization of work. 4. Measurement of small currents. Goals: Knowledges: Basic knowledges about interpretation of radiation quantities and units in metrology. The system of data processing and interpretation of results, including errors and uncertainties. Abilities: Process and evaluate the measured data according to appropriate standards of metrology. Identify the fundamentals of ionizing radiation. Requirements: Required prerequisities are 16ZDOZ12, 16DETE. Key words: metrology, value, gray, becquerel, sievert, proportional counter, liquide scintilator, beam of radiation, cavity ionizing chamber, electron equilbrium, X-ray spectra References Key references: [1] Sabol J., Introduction to metrology of ionizing radiation, Publisher CTU Prague 1982. (in Czech) Recommended references: [2] Act No. 505/1990 Coll. Metrology

Application of Ionizing Radiation in Analytical Methods16APLB Čechák - - 4+0 zk - 5

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

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

Introduction to Psychology00UPSY Hajíček - - 0+2 z - 1
 Course: Introduction to Psychology 00UPSY PhDr. Oudová Drahomíra Ph.D. - - - - 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.

Etika vědy a techniky00ETV Hajíček - - 0+2 z - 1
 Course: 00ETV PhDr. Hajíček Jakub Ph.D. - 0+2 Z - 1 Abstract: Outline: Outline (exercises): Goals: Requirements: Key words: References