The theory and application of mathematical methods for the physical sciences. Topics may include: vector calculus, linear algebra applied to coordinate transformations, probability distributions, systems of linear ordinary and partial differential equations and boundary value problems, Fourier analysis and orthogonal functions, the Heat and Wave equations in various coordinate systems, and the use of Legendre polynomials and Spherical Bessel functions. Computational methods and standard software tools will be used to solve complex physics problems.