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This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity. Green's function is a topic in partial differential equations and covered in most standard texts, while infinite products are used in mathematical analysis. For the two-dimensional Laplace equation, Green's functions are conventionally constructed by either the method of images, conformal mapping, or the eigenfunction expansion. The present text focuses on the construction of Green's functions for a wide range of boundary-value...

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's...

"Analyzes a wide range of problem classes originating in applied mechanics, stressing the use of influence (Green's) functions in their analysis. Provides an extensive list of influence functions and matrices-several in print for the first time. Addresses areas such as fluid flow, acoustics, electromagnetism, heat transfer, and elasticity."

Green's functions represent one of the classical and widely used issues in the area of differential equations.

This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations...