Topic 1: Analytical Methods I. Introduction to modern mathematics, real analysis of functions of one variable, linear algebra, elements of real analysis of functions of many variables, calculus of variations. Aerospace Engineering 380P (Topic 1) and Engineering Mechanics 386K may not both be counted.

Topic 2: Analytical Methods II. Elements of complex analysis, Fourier and Laplace transforms, ordinary and partial differential equations, perturbation methods. Only one of the following may be counted: Aerospace Engineering 380P (Topic 2), Computational Science, Engineering, and Mathematics 386L, Engineering Mechanics 386L.

Topic 4: Numerical Methods in Ordinary Differential Equations. One-step, multistep, and extrapolation methods for solving stiff and nonstiff equations; discretization errors and stability; computer solution of selected problems.