Partial Differential Equations
Solve partial differential equations in Cartesian, cylindrical, and spherical coordinates using separation of variables and expansions in orthogonal functions. Apply boundary conditions appropriate for physical systems.
Perform algebraic computations involving complex numbers and functions.
Use the properties (such as recursion relations, derivative relationships, and orthogonality conditions) of various special functions, including trigonometric functions, Bessel functions, and Legendre polynomials to solve problems involving those functions.
Use Fourier series and transforms to expand functions and solve partial differential equations on appropriate domains.