Calculus of Variations and Integral Equations
Topics in the calculus of variations, integral equations and applications.
Calculus of Variations - Mechanics, Control and other applications, MacCluer, Prentice-Hall, 2004.
This course will cover the following topics:
- Basic concepts of calculus of variations - convexity and Lagrange multipliers
- Formulating variational problems and examples: geodesics, the catenary, the brahistochrone, shapes of minimum resistance
- Euler Lagrange equations, the Hamiltonian point of view
- Constrained optimization problems - integral and nonintegral constraints. Euler Lagrange equations and applications
- Extremal surfaces - soap films, the Schrodinger equation
- Uniqueness for variational problems, first and second variations of functionals
- Weierstrass E function and Erdmann corner conditions
(Oh 2010 )