SubjectsSubjects(version: 953)
Course, academic year 2019/2020
Partial Differential Equations (PDE) - N413014
Title: Parciální diferenciální rovnice
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
Actual: from 2019 to 2020
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:
Guarantor: Axmann Šimon Mgr. Ph.D.
Class: Předměty pro matematiku
Is interchangeable with: M413008
Examination dates   Schedule   
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 (21.05.2019)
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, elementary calculus of variations.

Last update: Axmann Šimon (21.05.2019)
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 (21.05.2019)
Teaching methods -

Lectures take place according to the syllabus.

Last update: Axmann Šimon (21.05.2019)
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 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.

Last update: Axmann Šimon (23.05.2019)
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