Equations of Mathematical Physics

The course is not on the list Without time-table
Code Completion Credits Range Language
01RMFM Z,ZK 6 4P+2C Czech
Garant předmětu:
Department of Mathematics

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).

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:

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

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

Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-05-28
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