SubjectsSubjects(version: 953)
Course, academic year 2021/2022
Partial Differential Equations (PDE) - M413008
Title: Parciální diferenciální rovnice
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:3/0, Ex [HT]
Capacity: unlimited / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
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
Annotation -
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)
Aim of the course -

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)
Literature -

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)
Learning resources -

Last update: Axmann Šimon (23.05.2019)
Teaching methods -

Lectures and exercises take place according to the syllabus.

Last update: Kubová Petra (01.05.2019)
Syllabus -

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)
Registration requirements -

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)