Infinite dimensional vector spaces, especially Banach and Hilbert vector spaces. Orthogonal projections and the spectral decomposition theorem. Applications to differential equations and approximation methods. The intuitive beginnings and modern applications of key ideas of mathematics such as polyhedra and the fundamental theorem of algebra. Extensive use of computer-generated films to help visualize the methods and results.
Topics vary from term to term.
Course may be taken more than once. Newton's method, curve and surface fitting. Numerical solutions of differential equations and linear systems, eigenvalues and eigenvectors. Fast Fourier transform. Kalman and Nyquist criteria.