This is a course in ordinary differential equations. Topics include first order o.d.e.'s, linear second order o.d.e.'s, systems of differential equations, numerical methods and the Laplace transform. 0252. Orthogonal polynomials including Legendre and Chebyshev polynomials, Fourier series, partial differential equations, boundary value problems, the phase plane, stability, Liapunov's method, eigenvalue problems, and introduction to functions of a complex variable. Computer arithmetic, pitfalls of computation, iterative methods for the solution of a single nonlinear equation, interpolation, least squares, numerical differentiation, numerical integration, and solutions of linear systems by direct and iterative methods. In sections with 4 credits there is a required lab, where a computing lab is used to demonstrate topics and provide hands-on experience with the ideas encountered.
Activities designed to promote understanding are the primary focus.
Sections without the laboratory must be taken for 3 credits. 0254. Solution of systems of nonlinear equations, solution of initial value problems, matrix norms and the analysis of iterative solutions, numerical solution of boundary value problems and partial differential equations, and introduction to the finite element method. Approval of the department adviser and the instructor. Intensive study in a specific area. May be taken in either semester.