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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： J. David Logan著

出 版 社：

出版时间： 2004-5-1字数：版次： 1页数： 209印刷时间： 2004/05/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387209531包装： 平装内容简介

This textbook is for the standard，one-semester，junior-senior course that often goes by the title“Elementary Partial Differential Equations”or“Boundary Value Problems”。The audience consists of students in mathematics，engineering，and the physical sciences。The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains。The text differs from other texts in that it is a brief treatment; yet，it provides coverage of the main topics usually studied in the standard course as well as an introduction to using computer algebra packages to solve and understand partial differential equations。To give this text an even wider appeal，the 2nd edition has been updated with a new chapter on partial differential equation models in biology，and with various examples from the life sciences throughout the text。There are more exercises，as well as solutions and hints to some of the problems at the end of the book。

目录

Preface to the Second Edition

To the Student

Chapter 1：The physical origins of partial differential

1.1 Mathematical models

1.2 Conservation laws

1.3 Diffusion

1.4 PDEs in biology

1.5 Vibrations and acoustics

1.6 Quantum mechanics

1.7 Heat flow in three dimensions

1.8 Laplace’s equation

1.9 Classification of PDEs

Chapter 2 Partial differential equations on unbounded domains

2.1 Cauchy problem for the heat equation

2.2 Cauchy problem for the wave equation

2.3 Ill-posed problems

2.4 Semi-infinite domains

2.5 Sources and Duhamel’s principle

2.6 Laplace Transforms

2.7 Fourier Transforms

2.8 Solving PDEs Using Computer Algebra Systems

Chapter 3： Orthogonal Expansions

3.1 The Fourier Method

3.2 Orthogonal Expansions

3.3 Classical Fourier Series

3.4 Sturm-Liouville Problems

Chapter 4： Partial Differential Equations on Bounded Domains

4.1 Separation of Variables

4.2 Flux and Radiation Conditions

4.3 Laplace’s Equation

4.4 Cooling of a Sphere

4.5 Diffusion in a Disk

4.6 Sources on Bounded Domains

4.7 Parameter Identification Problems

4.8 Finite Difference Methods

Chapter 5： Partial Differential Equations in the Life Sciences

5.1 Age-Structured Models

5.2 Traveling Wave Fronts

5.3 Equilibria and Stability

Appendix： Ordinary Differential Equations

Table of Laplace Transforms

References

Index

 

 

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