| Course title | Applied partial differential equations |
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| Course code | UMB/751 |
| Organizational form of instruction | Lecture |
| Level of course | Master |
| Year of study | 3 |
| Frequency of the course | In each academic year, in the winter semester. |
| Semester | Winter |
| Number of ECTS credits | 2 |
| Language of instruction | Czech |
| Status of course | Compulsory-optional |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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Content of lectures: 1. Introduction - mathematical modelling of natural phenomena, basic concepts and physical principles, origin of partial differential equations 2. Conservation laws, constitutive equations, diffusion equations 3. Physics of diffusion - random walk, diffusion kernel 4. Phase delayed diffusion - modes of energy transport 5. Wave-particle duality - traveling wave, speed of light 6.-7. Steady processes vs steady states - energy transport, Laplace equation, cooling 8.-9. Energy transport induced by external influences - convolution, Laplace transform, problems of identifiability of system parameters 10. Impact of energy sources/consumption on energy transport processes, Green's function 11.-12. Selected quasi-linear phenomena and fractals - Schrödinger equation, quantum waves, shock waves, deterministic chaos, fractal measures 13.-14. Selected nonlinear phenomena - turbulence, ecology and epidemiology, flow, Navier-Stokes equations
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| Learning activities and teaching methods |
| unspecified |
| Learning outcomes |
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The course aims to introduce the student to the application of partial differential equations in physical and engineering sciences.
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| Prerequisites |
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Knowledge of physics (high school level) and ordinary differential equations (in the Introduction to Differential Equations course) at a basic level, knowledge of mathematical analysis at a more advanced level (in the Mathematical Analysis I-IV course).
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| Assessment methods and criteria |
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unspecified
Completion of the exam at the end of the semester |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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