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Course: Numerical Methods and Programming

Department/Abbreviation: OPT/NUM

Year: 2020

Guarantee: 'prof. Mgr. Jaroslav Řeháček, Ph.D.'

Annotation: Introduction to numerical methods and programming.

Course review:
1. Mathematica: basics of programming, symbolic calculations, data visualization. 2. Programming in Matlab/Octave a Oslo: comparison with C language, libraries, user functions. 3. Introduction to numerical methods: accuracy, truncation errors, stability. 4. Linear algebra: vectors and matrices, solving systems of linear equations, SVD, Cholesky decomposition. 5. Approximations: interpolation, extrapolation, interpolating polynomials, splines. 6. Numerical integration/derivation: elementary and advanced algorithms, multi-dimensional integration, integration of ordinary differential equations. 7. Nonlinear equations, root finding: bisection, false-position methods, Newton-Raphson method. 8. Optimizations: golden ratio method, Brent method, gradient methods, multi-dimensional optimization, downhill simplex method, conjugated directions, conjugated gradient, simulated annealing, linear programming. 9. Models: least-squares, estimation theory, nonlinear models, confidence intervals. 10. Fourier transform: continuous and discrete transforms, FFT algorithm and applications, Nyquist frequency, discrete Fourier transform in 2D and 3D. 11. Applications I: numerical simulation of optical signal propagation, Fresnel diffraction, sampling requirements, aliasing. 12. Applications II: analysis of imaging systems and aberrations, wavefront reconstruction.