Integral Equations: Basic concepts, Volterra integral equations, relationship between linear differential equations and Volterra equations, resolvent kernel, method of successive approximations, convolution type equations, Volterra equations of first kind, Abels integral equation, Fredholm integral equations, Fredholm equations of the second kind, the method of Fredholm determinants, iterated kernels, integral equations with degenereted kernels, eigenvalues and eigenfunctions of a Fredholm alternative, construction of Green's function for BVP, singular integral equations.
Calculus of variations: Euler-Lagrange equations, degenerate euler equations, Natural boundary conditions, transversality conditions, simple applications of variational formulation of BVP, minimum of quadratic functional. Approximation methods-Galerkin's method, weighted-residual methods, Colloation methods.Variational methods for time dependent problems. |