Course: Numerical Methods and Programming

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Course title Numerical Methods and Programming
Course code OPT/NMP
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Řeháček Jaroslav, prof. Mgr. Ph.D.
Course content
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.

Learning activities and teaching methods
Lecture, Demonstration
  • Preparation for the Course Credit - 20 hours per semester
Learning outcomes
Introduction to numerical methods and programming.
On successful completion of this module, students should be able to know and understand the syllabus topics and be able to use the acquired knowledge in solving problems.
Prerequisites
No prior requirements.

Assessment methods and criteria
Student performance, Dialog

Sufficient knowledge of the syllabus topics.
Recommended literature
  • Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. (1992). Numerical Recipes. Cambridge Univ. Press, Cambridge.
  • Schmidt J.D. (2010). Numerical Simulation of Optical Wave Propagation. SPIE Press.
  • Vitásek, E. (1987). Numerické metody. SNTL, Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Optics and Optoelectronics (2015) Physics courses 1 Winter
Faculty of Science Digital and Instrument Optics (1) Physics courses 1 Winter