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Course detail

Calculus of Variations

Course unit code: FSI-S1M
Academic year: 2016/2017
Type of course unit: compulsory
Level of course unit: Master's (2nd cycle)
Year of study: 1
Semester: summer
Number of ECTS credits:
Learning outcomes of the course unit:
The variational calculus makes access to mastering in a wide range
of classical results of variational calculus. Students get up apply results
in technical problem solutions.
Mode of delivery:
90 % face-to-face, 10 % distance learning
The calculus in the conventional ammount, boundary value problems of ODE and PDE.
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
The calculus of variations. The classical theory of the variational calculus: the first and the second variations, conjugate points, generalizations for a vector function, higher order problems, relative maxima and minima and isoperimaterical problems, integraks with variable end points, geodesics, minimal surfaces. Applications in mechanics and optics.
Recommended or required reading:
Fox, Charles: Introduction to the Calculus of Variations, New York: Dover, 1988
Kureš, Miroslav, Variační počet, PC-DIR Real Brno 2000
Kureš, Miroslav, Variační počet, PC-DIR Real, Brno 2000
Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Classified seminar credit: the attendance, the brief paper, the semestral work
Language of instruction:
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Students will be made familiar with fundaments of variational calculus. They will be able to apply it in various engineering tasks.
Specification of controlled education, way of implementation and compensation for absences:
Seminars: required
Lectures: recommended

Type of course unit:

Lecture: 26 hours, optionally
Teacher / Lecturer: doc. RNDr. Miroslav Kureš, Ph.D.
Syllabus: 1. Introduction. Instrumental results.
2. The fundamental lemma. First variation. Euler equation.
3. Second variation.
4. Classical applications.
5. Generalizations of the elementary problem.
6. Methods of solving of first order partial differential equations.
7. Canonical equations and Hamilton-Jacobi equation.
8. Problems with restrictive conditions.
9. Isoperimetrical problems.
10. Geodesics.
11. Minimal surfaces.
12. n-bodies problem.
13. Solvability in more general function spaces.
seminars: 13 hours, compulsory
Teacher / Lecturer: doc. RNDr. Miroslav Kureš, Ph.D.
Syllabus: Seminars related to the lectures in the previous week.

The study programmes with the given course