| Course title | Numerical Methods and Programming |
|---|---|
| Course code | OPT/NUM |
| 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) |
|---|
|
| 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
|
| 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 |
|
| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Optics and Optoelectronics (2021) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): General Physics and Mathematical Physics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Digital and Instrument Optics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |