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The purpose of this book is to provide research workers in applied mathematics, physics and engineering with practical methods for solving systems of nonlinear partial differential equations. The first two chapters provide an introduction to the more or less classical results of Lie dealing with symmetries and similarity solutions. The results, however, are presented in the context of a contact manifold rather than the usual jet bundle formulation and provide a number of new conclusions. The remaining three chapters present essentially new methods of solution that are based on recent...

This is a reprint of the 1985 edition pubished by John Wiley & Sons. Edelen (mathematics emeritus, Lehigh U.) believes the exterior calculus is essential, if not for its intrinsic value, then because in the quantified sciences it has become an expository vehicle. He proves his point by examining the exterior calculus in terms of its vectors and for

Theoretical researches in general relativity and observational data from galactic astronomy combine in this volume in contributions to one of the oldest questions of natural philosophy: Is the structure of the physical world more adequately described by a continuous or a discrete mode of representation? Since the days of the Pythagoreans, this question has surfaced from time to time in various guises in science as well as in philosophy. One of the most bitterly contested and illuminating controversies between the continuous and the discrete viewpoints is to be found in the wave versus...