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Introduction

Part of the Texts in Applied Mathematics book series (TAM, volume 45)

Abstract

In this first chapter we begin in Sect. 1.1 by introducing the partial differential equations and associated initial and boundary value problems that we shall study in the following chapters. The equations are classified into elliptic, parabolic, and hyperbolic equations, and we indicate the corresponding type of problems in physics that they model. We discuss briefly the concept of a well posed boundary value problem, and the various techniques used in our subsequent presentation. In Sect. 1.2 we introduce some notation and concepts that will be used throughout the text, and in Sect. 1.3 we include a detailed derivation of the heat equation from physical principles explaining the meaning of all terms that occur in the equation and the boundary conditions. In the problem section, Sect. 1.4, we add some further illustrative material.

Keywords

Constitutive Relation Heat Equation Biot Number Divergence Theorem Time Dependent Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

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