Every problem of the calculus of variations
has a solution,
provided that the word `solution'
is suitably understood. David Hilbert
Clear and elegant methods of modern Calculus of Variations allow to solve large number of problems in Science and Engineering.
Originated by Bernoulli, Newton, Euler, and systematically developed beginning from XVIII century, these days Calculus of Variations attracts attention of mathematicians and provides new tools to find the best possible solutions,
and to understand the essence of optimality.
Topics to be covered:
Basic techniques of Calculus of Variations. Euler equations, Legendre and Weierstrass tests, direct methods.
Hamiltonian.
Duality and Legendre transform.
Variational principles.
Variational problems for multiple integrals:
Optimization of shape of domains
Variational problems for multiple integrals:
Ill-posed problem. Introduction to relaxation.
:
Addressed to graduate and to senior undergraduate students in math and science.