Second order equations in n dimension: classification, canonical form, characteristic surfaces. Laplace equation as a representative of the elliptic equation: the mean value theorem, fundamental solutions and Green functions, the boundary value problems. Wave equation as a representative of hyperbolic equations: initial value problems, the d'Alambert formula, the method of descent, propagation of singularities, Duhamel's principle. Heat equation as a representative of parabolic equations: initial value problems. Introduction to integral transforms: Fourier, Laplace, Hankel transforms. Prerequisite: MATH 337.