Chapter one

Preliminary Mathematical Knowledge

Abstract

This chapter gives a brief elementary description of the basic mathematical tools that will be employed throughout the book in developing the BEM for plates. It presents the Gauss-Green theorem and its application to derive the Gauss divergence theorem, the Green’s reciprocal identity and, in general, the reciprocal identity for a given linear differential operator. It also introduces Dirac’s delta function and describes its basic properties used for the derivation of the integral representation of the solution of a partial differential equation. The chapter concludes with a section on calculus on variations, which provides the reader with an efficient mathematical tool to derive the governing ...

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