CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Equations of Mathematical Physics

Code Completion Credits Range Language
01RMAF Z,ZK 7 4P+2C Czech
Garant předmětu:
Václav Klika
Lecturer:
Václav Klika
Tutor:
Lukáš Heriban, Václav Klika, Václav Růžek, Matěj Tušek
Supervisor:
Department of Mathematics
Synopsis:

The subject of this course is solving integral equations, theory of generalized functions, classification of partial

differential equations, theory of integral transformations, and solution of partial differential equations (boundary value

problem for eliptic PDE, mixed boundary problem for eliptic PDE).

Requirements:
Syllabus of lectures:

1. Introduction to functional analysis - factor space, Hilbert space, scalar product, orthonormal basis, fourier series,

orthogonal polynoms, hermite operators, operator spectrum and its properties, bounded operators, continuous operators,

eliptic operators

2. Integral equations - integral operator and its properties, separable kernel of operator, sequential approximation

method, iterated degenerate kernel method, Fredholm integral equations, Volterra integral equations.

3. Classification of partial differential equations - definitions, types of PDE, transformations of partial differential

equations into normal form, classification of PDE, equations of mathematical physics.

4. Theory of generalized functions - test functions, generalized functions, elementary operations in distributions,

generalized functions with positive support, tensor product and convolution, temepered distributions.

5. Theory of integral transformations - classical and generalized Fourier transformation, classical and generalized

Laplace transform, applications.

6. Solving differential equations - fundamental solution of operators, solutions of problems of mathematical physics.

7. Boundary value problem for eliptic partial differential equation.

8. Mixed boundary problem for eliptic partial differential equation.

Syllabus of tutorials:
Study Objective:
Study materials:

Key references:

[1] A. G. Webster, Partial Differential Equations of Mathematical Physics, Second Edition, Dover, New York, 2016

[2] A. Tikhonov, A. Samarskii: Equations of Mathematical Physics, Courier Corp., Science, 2013

Recommended literature:

[5] L. Schwartz: Mathematics for the Physical Sciences, Dover Publication, 2008.

[6] I. M. Gel'fand, G. E. Shilov: Generalized Functions. Volume I: Properties and Operations, Birkhäuser Boston, 2004.

Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-20
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