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Course: Computer Physics

Department/Abbreviation: SLO/SZZFP

Year: 2020

Guarantee: 'doc. RNDr. Ondřej Haderka, Ph.D.'

Annotation: Final exam for verification and evaluation of the level of knowledge.

Course review:
PROGRAMMING AND LABORATORY TECHNOLOGY - The basic elements of the language C, control structures, input and output, standard libraries, files, disk operations, functions, pointers and data structures. - Objects and classes in C++, pointers, constructors and destructors, inheritance, polyformismus, streams, template classes. - Matlab - working platform and its configuration, basic and special mathematical functions. The programming language of Matlab. Matrix operations. Data analysis and Fourier transform, statistical variables, filtering, convolution, interpolation, polynomials. 2D and 3D charts, bar charts, work with graphic objects. Data types, import and export data, operations with text strings. - Digital measuring system, basic classsification and construction, structure (bus, star, ring, tree), centralized/decentralized measuring systems, open/closed measuring systems, laboratory measuring systems, standardization of instrument interfaces. - Standard interface, RS-232, RS-485, IEEE 488, USB, IEEE 1394 modular systems, industrial systems, VME, VXI, CompactPCI, PXI, PC/104, MXI, instrumental interfaces of industrial measuring systems, Foundation Fieldbus, Profibus, CAN. - Method of processing and storing data in measuring systems, sampling. Triggering a detection logic. - Types of communication protocols (RTU, ASCII, datagrams) and their properties, types of checksums (LRC, CRC16, CRC32). - Function of controlling software, serialization of requests/inquiries to the device, the control method of running software as a service/daemon. - Methods of remote experiment control via SSH, TCP / IP, VNC. - Data formats for storing data - binary, XML, SQL, ASCII, CSV, data parsing. NUMERICAL METHODS - Algebraic methods - systems of linear algebraic equations, tridiagonal scheme, Gauss and Gauss-Jordan method, LU decomposition, matrix inversion. - Eigenvalues and eigenvectors of matrices - a general problem, symmetric matrices, LU and QR algorithm, iterative algorithms. - The roots of polynomials - Lin-Bairstow method, Siljakov coefficients, Laguerre method. - Solving systems of nonlinear equations - interval bisection, Newton's method of tangents, Richmond method of tangential hyperboles, their generalization to systems of equations, Chebyshev iterative methods, Warner scheme, gradient methods, the method of iteration. - Interpolation - Laguerre polynomial, Newton polynomial, the best trigonometric polynomial, cubic splines, Chebyshev approximations (Remez algorithm), Fourier series. - Numerical differentiation and integration - trapezoidal formula, Newton-Cotes formulas, Simpson's formula, Gauss method, special formula. - Minimization of functions and optimization - minimization of functions of one variable (the golden section, the differential methods), the simplex method of minimization of functions of several variables, gradient method (method of conjugate vectors, Powell's quadratically convergent method), linear programming, combinatorial problems. - Numerical solution of ordinary differential equations - problem with initial condition (Euler's method, Runge-Kutta methods, Merson's method, stability, convergence, correctness), boundary problem (shooting method, linear systems of differential equations, analytical solutions, problems of existence of numerical solution), methods of networks - differential method (differential scheme for nonlinear equations, construction of difference schemes, Marčukov's identity). - Discrete and fast Fourier transform and its applications. - Solution of partial differential equations - initial and boundary conditions, the finite difference methods, finite element methods, variational principle, Galerkin method, spectral method. - Algorithms for working with sparse matrices - representation and methods for working with sparse matrices. - Random numbers - pseudo-random number generation, uniform distribution, normal distribution - Special functions - Gamma function, beta function, factorial, binom