Lectures in Applied Mathematics 1964; 343 pp; softcover Volume: 3 Reprint/Revision History: ninth printing 1998 ISBN10: 0821800493 ISBN13: 9780821800492 List Price: US$54 Member Price: US$43.20 Order Code: LAM/3.1
 This book consists of two main parts. The first part, "Hyperbolic and Parabolic Equations", written by F. John, contains a wellchosen 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, Hilbertspace methods, and potentialtheoretic methods. It also contains a brief discussion of some quasilinear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations. Readership Graduate students and research mathematicians interested in partial differential equations. Table of Contents 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
 Quasilinear equations
 Supplement I. Eigenvalue expansions
 Supplement II. Parabolic equations
 Index
