Study of partial differential equations, which play a central role in our understanding of the natural world. Basic problems of heat transfer, fluid dynamics, vibrations of solids, electromagnetism, quantum mechanics, theories of the economy, etc., all require solutions of partial differential equations. This course focuses on analytical techniques for solving the three classical types of equations representing the physical phenomena of wave propagation, diffusion, and equilibrium. Most courses 4000- level and above can be credited to all degree programs.
All courses are subject to advisor approval.
Initial and boundary value problems. Separation of variables. Eigenvalue problems and orthogonality of eigenfunctions. Solutions in one, two and three dimensions. Cartesian, cylindrical, and spherical coordinate systems.