MATH 542

Elements of Partial Differential Equations

Theory of partial differential equations emphasizing the basic nature of solutions of hyperbolic, parabolic, and elliptic equations as represented, respectively, by the wave, heat, and Laplace equations. Solution techniques covered include the method of characteristics, separation of variables, generalized eigenfunction expansions, and the Fourier integral and transform. Theoretical approaches are presented for the following topics: convergence and uniform convergence of Fourier series, Bessels inequality, Greens identities, Sturm-Liouville theory, uniqueness of solutions, existence of fundamental solutions, and the maximum principle

Units: 3.0