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Last update: Axmann Šimon Mgr. Ph.D. (21.05.2019)
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Last update: Axmann Šimon Mgr. Ph.D. (21.05.2019)
Students will master the basic theory of PDR: classification of PDR of the 2nd order, heat equation, wave equation, Laplace equation, method of characteristics for equations of the 1st order, elementary calculus of variations. |
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Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)
R: Turzík a kol.: Matematika II ve strukturovaném studiu, skripta, VŠCHT Praha, 2005, ISBN 80-7080-555-2 R: A. Klíč, M. Kubíček: Matematika III. Diferenciální rovnice, skripta, VŠCHT Praha, 1992, ISBN 92-83-39/92 R: M. Dont: Úvod do parciálních diferenciálních rovnic, skripta, ČVUT Praha, 2008, ISBN 978-80-01-04095-9 A: L. C. Evans: Partial Differential Equations, American Mathematical Society, 1998, ISBN 08-2180-772-2 A: C. Constanda: Solution Techniques for Elementary Partial Differential Equations. Chapman & Hall/CRC mathematics, 2002, ISBN 1-58488-257-3 A: R. E. Mickens: Mathematical Methods for the Natural and Engineering Sciences. World Scientific Publishing Co. Pte. Ltd., 2004, ISBN 981-238-750-1 |
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Last update: Axmann Šimon Mgr. Ph.D. (21.05.2019)
web.vscht.cz/~axmanns/PDR/main.html www.vscht.cz/mat/MCHI/PoznamkyMCHI.html |
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Last update: Axmann Šimon Mgr. Ph.D. (21.05.2019)
Lectures take place according to the syllabus. |
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Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)
1. Introduction, classical solution. 2. Elements of vector analysis, general balance law. 3. First order linear differential equations, method of characteristics. 4. Characteristic directions. Classification of linear second order equations. 5. Wave equation. 6. Initial-boundary value problems for wave equation 7. Heat equation. 8. Heat equation in bounded domains. 9. Laplace equation 10. Fourier series. 11. Separation of variables. 12. Elements of functional analysis 13. Calculus of variations, Euler-Lagrange equation. 14. Weak solutions. |
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Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)
We assume the knowledge of mathematical analysis, corresponding for example to the lectures Mathematics A and Mathematics B. The knowledge of function series and basic functional analysis is advantage. |
Teaching methods | ||||
Activity | Credits | Hours | ||
Účast na přednáškách | 1 | 28 | ||
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi | 1.5 | 42 | ||
Příprava na zkoušku a její absolvování | 1.5 | 42 | ||
Účast na seminářích | 1 | 28 | ||
5 / 5 | 140 / 140 |
Coursework assessment | |
Form | Significance |
Regular attendance | 40 |
Examination test | 30 |
Oral examination | 30 |