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Partial differential equations appear in models of fluid flow, gravity, quantum mechanics, heat flow, etc. The course covers the classical theory of linear PDEs. We will study the second order PDEs (the heat equation, the wave equation, and Laplace’s equation) and we will describe first order equations via the method of characteristics.
Last update: Axmann Šimon (23.05.2019)
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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. Last update: Axmann Šimon (23.05.2019)
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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 Last update: Axmann Šimon (23.05.2019)
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Lectures and exercises take place according to the syllabus. Last update: Kubová Petra (01.05.2019)
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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. Last update: Axmann Šimon (23.05.2019)
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web.vscht.cz/~axmanns/PDR/main.html www.vscht.cz/mat/MCHI/PoznamkyMCHI.html Last update: Axmann Šimon (23.05.2019)
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We assume basic 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 advantageous. Last update: Axmann Šimon (23.05.2019)
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