A unique text and reference for pure and applied mathematicians, engineers, physicists, and chemists, this book was a landmark in the literature of computational methods in mathematical physics in the twentieth century. The treatment remains of great interest because of its thoroughness and scope. A valuable historic source for methods and approaches to problems of mathematical physics, this text is enhanced by many detailed, worked-out examples. Topics include methods based on the representation of the solution as an infinite series, the approximate solution of the integral equations of Swedish mathematician Erik Ivar Fredholm, the method of nets, and variational methods. Additional subjects include the conformal transformation of regions, principles of the application of conformal transformation to the solution of the fundamental problems for canonical regions, and Polish mathematician Dr. Hermann Schwarz's method.

The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non linear cases even for strong nonlinearities, and also for deterministic or stochastic cases - again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations.