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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Variational Methods

The course is not on the list Without time-table
Code Completion Credits Range Language
01VME ZK 2 2P+0C Czech
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

1. Functional extremum, Euler equations.

2. Conditions for functional extremum.

3. Theorem on the minimum of a quadratic functional.

4. Construction of minimizing sequences and their convergence.

5. Choice of basis.

6. Sobolev spaces.

7. Traces. Weak formulation of the boundary conditions.

8. V-ellipticity. Lax-Milgram theorem.

9. Weak solution of boundary-value problems.

Requirements:
Syllabus of lectures:

1. Functional extremum, Euler equations.

2. Conditions for functional extremum.

3. Theorem on the minimum of a quadratic functional.

4. Construction of minimizing sequences and their convergence.

5. Choice of basis.

6. Sobolev spaces.

7. Traces. Weak formulation of the boundary conditions.

8. V-ellipticity. Lax-Milgram theorem.

9. Weak solution of boundary-value problems.

Syllabus of tutorials:
Study Objective:
Study materials:

Povinná literatura

1. S. V. Fomin, R. A. Silverman: Calculus of variations, Courier Dover Publications, Dover, 2000.

2. K. W. Cassel, Variational Methods with Applications in Science and Engineering, Cambridge University Press, 2013.

Doporučená literatura

3. B. S. Mordukhovich: Variational Analysis and Applications, Springer International Publishing, 2018.

4. F. J. Sayas, T. S. Brown and M. E. Hassell, Variational Techniques for Elliptic Partial Differential Equations : Theoretical Tools and Advanced Applications, Taylor and Francis, 2019

5. B. Dacorogna: Introduction to the Calculus of Variations, Imperial College Press, London, 2004.

6. B. Van Brunt: The calculus of variations, Birkhäuser, Basel, 2004.

7. E. Giusti: Direct methods in the calculus of variations, World Scientific, Singapore, 2003.

Note:
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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