Course detail
Calculus of Variations
FSI-S1M-AAcad. year: 2025/2026
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.
Language of instruction
Number of ECTS credits
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Mode of study
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Department
Entry knowledge
Rules for evaluation and completion of the course
Seminars: required
Lectures: recommended
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.
Exercise
Teacher / Lecturer
Syllabus