This book consists of two main parts. The first part, ""Hyperbolic and Parabolic Equations"", written by F. John, contains a well-chosen assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. The emphasis is on illustrating the subject without attempting to survey it. The point of view is classical, and this serves well in furnishing insight into the subject; it also makes it possible for the lectures to be read by someone familiar with only the fundamentals of real and complex analysis.The second part, ""Elliptic Equations"", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations.
Part I. Hyperbolic and Parabolic Equations: Equations of hyperbolic and parabolic types The wave operator Cauchy's problem, characteristic surfaces, and propagation of discontinuities Linear hyperbolic differential equations A parabolic equation: The equation of heat conduction Approximation of solutions of partial differential equations by the method of finite differences; Part II. Elliptic Equations: Elliptic equations and their solutions The maximum principle Hilbert space approach. Periodic solutions Hilbert space approach. Dirichlet problem Potential theoretical approach Function theoretical approach Quasi-linear equations Supplement; I. Eigenvalue expansions Supplement; II. Parabolic equations Index.