Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods.
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. This is a Graduate level course.