Partial Differential Equations II.

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

An introductory course in modern methods of partial differential equations.

Requirements:

Syllabus of lectures:

Banach spaces. Linear operators and functionals in Banach spaces, the Banach fix point theorem. Hilbert spaces. Fourier series, the Riesz theorem. the fix point theorem for positively definite operators. Distributive derivatives. Spaces of functions, Sobolev spaces. The weak formulation of a boundary problem for linear equations of the second order. The Lax-Milgram lemma. Existence of weak solutions of the elliptic boundary problems. The minimum of quadratic functionals. Approximation of weak solutions: the Galerkin method, the Ritz method.

Syllabus of tutorials:

Banach spaces. Linear operators and functionals in Banach spaces, the Banach fix point theorem. Hilbert spaces. Fourier series, the Riesz theorem. the fix point theorem for positively definite operators. Distributive derivatives. Spaces of functions, Sobolev spaces. The weak formulation of a boundary problem for linear equations of the second order. The Lax-Milgram lemma. Existence of weak solutions of the elliptic boundary problems. The minimum of quadratic functionals. Approximation of weak solutions: the Galerkin method, the Ritz method.

Study Objective:

Study materials:

[1] Karel Rektorys: Variational methods in mathematics, science and engineering. D. Reidel Publishing Company, Dordrecht 1977, 571 pp. ISBN 90-277-0488-0.

[2] Michael Renardy, Robert C. Rogers: An introduction to partial differential equations. Springer-Verlag 1992, 430 pp. ISBN 0-387-97952-2.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: