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Calculus of Variations and Integral Equations

648

Topics in the calculus of variations, integral equations and applications.

Text: 

Calculus of Variations - Mechanics, Control and other applications, MacCluer, Prentice-Hall, 2004.

Prerequisite: 

MATH 220 , MATH 223 and MATH 290, or MATH 320.

Credit Hours: 
3

This course will cover the following topics:

  1. Basic concepts of calculus of variations - convexity and Lagrange multipliers
  2. Formulating variational problems and examples: geodesics, the catenary, the brahistochrone, shapes of minimum resistance
  3. Euler Lagrange equations, the Hamiltonian point of view
  4. Constrained optimization problems - integral and nonintegral constraints. Euler Lagrange equations and applications
  5. Extremal surfaces - soap films, the Schrodinger equation
  6. Uniqueness for variational problems, first and second variations of functionals 
  7. Weierstrass E function and Erdmann corner conditions

(Oh 2010 )

Frequency: 
Every Spring Semester

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