Variational Calculus and Its Applications

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

In the course we acquaint students with foundations of variational calculus. As the methods of this calculus are mostly expanded in physics, we concentrate especially to applications in this branch. Firstly we remind basic physical principles of mechanics known from lectures about physics and mechanics. Next we show the connection of Lagrangian equations for extreme with Eulerian equations for extreme of functional. Obtained Hamiltonian principle we apply to some problems of mechanics of mass points, continuum mechanics and field theory. Finally we use methods of variational calculus to some problems solved in other branches of science.

Requirements:

Differential and integral calculus of the functions of several variables, differential equations.

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Knowlegde of basic ideas of variational calculus and its application in formulation of its physical principle and finding the extremal values of the functionals.

Study materials:

Fučík S., Nečas J., Souček V.: Úvod do variačního počtu, Praha, SPN, 1972, Kureš M.: Varirační počet, ČUT Brno, 2000, Rektorys K.: Variační metody v inženýrských problémech a problémech matematické fyziky, Praha, SNTL, 1974, Dacorogna B.: Direct methods in the calculus of variations, Springer-Verlag Berlin, 1989.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: