MA 631 Calculus of Variations
The course aims to introduce the students to the theory and methods of calculus of variations with application to mechanics, physics, and chemistry. Calculus of variations deals with minimizing or maximizing functionals that may depend on several functions and their derivatives subject to various constraints on those functions. Functionals frequently arise from physical principles; examples include the least action principle, maximal entropy principle, Fermats principle in optics. The calculus of variations has applications in many areas: differential geometry (minimal surfaces, geodesic problem), geometric optics, elastic media (string, beam and membrane), dynamics of particles, entropy maximization, optimal path planning with various objectives and constraints, shape optimization in linear continuum mechanics, to name just a few.