Synopses & Reviews
The main purpose of this book is to provide a self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects. A variety of classical application topics are presented in physics, quantum mechanics, elasticity and fluid dynamics. Additional applications include maximum principle, Cauchy problem, heat and wave potentials, wave propagation, anisotropy, porous media, piezocrystal waves, plate bending, and boundary element methods. Computational components receive special attention throughout the book. The book offers an accessible and up-to-date survey for advanced students, researchers and scientists in applied mathematics, mathematical physics, engineering and the physical sciences. Features: Extensive applications topics presented in detail, with numerous worked examples â¿¢ Coverage of over 70 different differential operators and derivation of fundamental solutions for them by using Fourier transforms and the theory of distributions â¿¢ Computational components discussed in all relevant topics and applications
Review
"Kythe explores fundamental solutions of both linear and nonlinear differential operators from mathematical physics, elasticity, fluid dynamics, piezoelectrics, and cosmology. The book begins with a historical development of the subject.... Three appendices provide background on Fourier and Laplace transforms, details about several computer programs that can be used in conjunction with the book, and a listing of 76 differential operators. Extensive bibliography." --Choice
Synopsis
Overview Many problems in mathematical physics and applied mathematics can be reduced to boundary value problems for differential, and in some cases, inte grodifferential equations. These equations are solved by using methods from the theory of ordinary and partial differential equations, variational calculus, operational calculus, function theory, functional analysis, probability theory, numerical analysis and computational techniques. Mathematical models of quantum physics require new areas such as generalized functions, theory of distributions, functions of several complex variables, and topological and al gebraic methods. The main purpose of this book is to provide a self contained and system atic introduction to just one aspect of analysis which deals with the theory of fundamental solutions for differential operators and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related applicable and computational features. The sub ject matter of this book has its own deep rooted theoretical importance since it is related to Green's functions which are associated with most boundary value problems. The application of fundamental solutions to a recently devel oped area of boundary element methods has provided a distinct advantage in that an integral equation representation of a boundary value problem is often x PREFACE more easily solved by numerical methods than a differential equation with specified boundary and initial conditions. This situation makes the subject more attractive to those whose interest is primarily in numerical methods."
Synopsis
The book offers an accessible and up-to-date survey for advanced students, researchers and scientists in applied mathematics, mathematical physics, engineering and the physical sciences.
Synopsis
A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.