: Expanding functions in terms of orthonormal systems, such as Legendre, Hermite, and Laguerre polynomials.
: Deriving approximate solutions for linear and nonlinear differential equations. Key tools include Green's functions for solving inhomogeneous boundary value problems. Advanced mathematical methods with Maple
: Developing systematic ways to find approximate solutions to problems that cannot be solved exactly by starting from the exact solution of a related, simpler problem. : Expanding functions in terms of orthonormal systems,