Kernel Functions and Elliptic Differential Equations in Mathematical Physics
This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.
The two-part treatment begins with a survey of boundary value problems occurring in certain branches of theoretical physics. It introduces fundamental solutions in a heuristic way and examines their physical significance. Many concepts can be unified by concentrating upon these particular kernels, and the text explains the common mathematical background of widely varying theories, such as those of heat conduction, hydrodynamics, electrostatics, magnetostatics, and elasticity. In addition to its intrinsic interest, this material provides illustrations and exact mathematical formulation of the problems and the methods. The second part is confined to a rather special type of partial differential equation, which is dealt with in the greatest detail so that students can make applications and generalizations to similar problems.
"1007348951"
Kernel Functions and Elliptic Differential Equations in Mathematical Physics
This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.
The two-part treatment begins with a survey of boundary value problems occurring in certain branches of theoretical physics. It introduces fundamental solutions in a heuristic way and examines their physical significance. Many concepts can be unified by concentrating upon these particular kernels, and the text explains the common mathematical background of widely varying theories, such as those of heat conduction, hydrodynamics, electrostatics, magnetostatics, and elasticity. In addition to its intrinsic interest, this material provides illustrations and exact mathematical formulation of the problems and the methods. The second part is confined to a rather special type of partial differential equation, which is dealt with in the greatest detail so that students can make applications and generalizations to similar problems.
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Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

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Overview

This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.
The two-part treatment begins with a survey of boundary value problems occurring in certain branches of theoretical physics. It introduces fundamental solutions in a heuristic way and examines their physical significance. Many concepts can be unified by concentrating upon these particular kernels, and the text explains the common mathematical background of widely varying theories, such as those of heat conduction, hydrodynamics, electrostatics, magnetostatics, and elasticity. In addition to its intrinsic interest, this material provides illustrations and exact mathematical formulation of the problems and the methods. The second part is confined to a rather special type of partial differential equation, which is dealt with in the greatest detail so that students can make applications and generalizations to similar problems.

Product Details

ISBN-13: 9780486154657
Publisher: Dover Publications
Publication date: 12/26/2012
Series: Dover Books on Mathematics
Sold by: Barnes & Noble
Format: eBook
Pages: 464
File size: 26 MB
Note: This product may take a few minutes to download.

Table of Contents

Preface
Note to the Reader
A. Boundary Value Problems for Partial Differential Equations of Elliptic Type
1. Theory of Heat Conduction
2. Fluid Dynamics
3. Electro- and Magnetostatics
4. Elasticity
B. Kernel Function Methods in the Theory of Boundary Value Problems
1. Properties of Solutions
2. The Kernel Functions and Their Properties
3. Variational and Comparison Theory
4. Existence Theory
5. Dependence of Kernels on Boundary Conditions and the Differential Equation
6. Generalizations
List of Symbols Used in Part B
Bibliography
Author Index
Subject Index
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