Methods and theory for ordinary and partial differential equations. Review of eigenvectors and eigenmodes in solutions to systems of ordinary differential equations. The principle of linear superposition and eigenfunction expansion, orthogonality, and inner product on a vector space of functions. The method of separation of variables in rectangular and cylindrical coordinate systems; sinusoidal and Bessel orthogonal functions. The wave, diffusion, and Laplace’s (potential) equation. Sturm-Liouville theory: eigenvalue problems and orthogonal functions. Fourier transform and, time permitting, Laplace transform techniques. (28/0/0/14/0) PREREQUISITES: MTHE 227 (MATH 227) or MTHE 280 (MATH 280), MATH 226 or MTHE 237 (MATH 237) or MTHE 232 (MATH 232), or permission of the instructor
