Partial Differential Equations (PDE) - M413008
Title: Parciální diferenciální rovnice
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:3/0 Ex [hours/week]
Capacity: unlimited / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type:  
Additional information:
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Axmann Šimon Mgr. Ph.D.
Class: Předměty pro matematiku
Interchangeability : N413014
Examination dates   
Annotation -
Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)
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.
Aim of the course -
Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)

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.

Literature -
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

Learning resources -
Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)

Teaching methods -
Last update: Kubová Petra Ing. (01.05.2019)

Lectures and exercises take place according to the syllabus.

Syllabus -
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.

Registration requirements -
Last update: Axmann Šimon Mgr. Ph.D. (23.05.2019)

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.