• Fourier Series: This course is devoted to the use of Fourier series and other orthogonal expansions in the solution of initial- value and boundary-value problems for second-order linear partial differential equations. Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; eigenfunction expansions; spherical and cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace’s method, steepest descent); Laplace’s equation and harmonic functions, including the maximum principle. (MATH 454) (Back)