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PřF:M6800 Calculus of Variations - Course Information

## M6800 Calculus of Variations

**Faculty of Science**

Spring 2007

**Extent and Intensity**- 2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
**Supervisor**- prof. RNDr. Roman Šimon Hilscher, DSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Contact Person: prof. RNDr. Roman Šimon Hilscher, DSc. **Timetable**- Tue 13:00–14:50 UP2
**Prerequisites**- Differential and integral calculus of functions of one and several variables, linear algebra.
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**Fields of study the course is directly associated with**- there are 15 fields of study the course is directly associated with, display
**Course objectives**- Elemantary course in calculus of variations. The content copies the classical differential calculus of functions in infinite dimension. The focus are necessary and sufficient conditions for (weak) extrema in such problems.
**Syllabus**- Functional, simple variational problems, function spaces, variation of a functional, necessary conditions for an extremum, Euler's equation, fixed and variable endpoints. Second variation, sufficient conditions for an extremum. Discrete calculus of variations.

**Literature**- GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN.
*Calculus of variations*. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000. vii, 232 s. ISBN 0-486-41448-5. info *A history of analysis*. Edited by Hans Niels Jahnke. Providence: American Mathematical Society, 2003. ix, 422 s. ISBN 0-8218-2623-9. info- MORSE, Marston.
*The calculus of variations in the large*. New York: American Mathematical Society, 1934. ix, 368 s. ISBN 0-8218-1018-9. info

- GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN.
**Assessment methods**(in Czech)- Two-hour written final exam with. Oral evaluation of the exam with each student.
**Language of instruction**- English
**Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (Spring 2007, recent)
- Permalink: https://is.muni.cz/course/sci/spring2007/M6800