偏微分方程教程（英文版·第2版）|经典原版书库|（美）纳克莱 H.亚斯马|机械工业出版社

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偏微分方程教程（英文版·第2版）

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原书名：Partial Differential Equations and Boundary Value Problems with Fourier Series (2nd Edition)	原出版社：Prentice Hall/Pearson
作者：（美）纳克莱 H.亚斯马	出版社：机械工业出版社
译者：	丛书名：经典原版书库
出版日期：2005-5-1	上架日期：2005-10-8
ISBN：7111159128	页数：版次：1-1
开本：16开	装帧：

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| 大封面 | 封底 | 前言 | 内容简介 | 序言 | 目录 | 作者简介 | 译者简介 | 作者序 | 译者序 |

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内容简介
本书通过大量丰富的实例，帮助读者实现从基本的常微分方程向更多高级概念(偏微分方程、傅里叶级数和边界值问题等)的顺利过渡。作者轻松的语言风格使得书中的材料通俗易懂，尤其适合那些渴望了解更多和更深微积分知识的读者。

本书在第1版的基础上增加了偏微分方程在工程和物理学方面的应用，并且提供了更多数学证明和偏微分方程的原理。此外，本书的每一小节后都配备了大量的习题，并在页边提供了注释、图标或重要的公式等，突出了书中的重点与难点，方便读者自学。

本书提倡读者利用计算机辅助学习，旨在使读者更直观、更清晰地理解和掌握书中所讲述的题材。读者可以利用从作者网站上下载的Mathematica文件进行上机实践。

目录
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前言       iii
A Preview of Applications and Techniques
1.1 What Is a Partial Differential Equation?  2
1.2 Solving and Interpreting a Partial Differential Equation
2  Fourier Series        17
2.1 Periodic Functions  18
2.2 Fourier Series  26
2.8 Fourier Series of Functions with Arbitrary Periods  38
2.4 Half-Range Expansions: The Cosine and Sine Series  50
2.5 Mean Square Approximation and Parseval's Identity  53
2.6 Complex Form of Fourier Series  60
2.7 Forced Oscillations  69
Supplement on Convergence
2.8 Proof of the Fourier Series Representation Theorem  77
2.9 Uniform Convergence and Fourier Series  85
2.10 Diriehlet Test and Convergence of Fourier Series  94
3  Partial Differential Equations in Rectangular Coordinates  103
3.1 Partial Differential Equations in Physics and Engineering  104
3.2 Modeling:  Vibrating Strings and the Wave Equation  109
3.3 Solution of the One Dimensional Wave Equation:The Method of Separation of Variables  114
3.4 D'Alembert's Method  126
3.5 The One Dimensional Heat Equation  135
3.6 Heat Conduction in Bars: Varying the Boundary Conditions  146
3.7 The Two Dimensional Wave and Heat Equations  155
3.8 Laplace's Equation in Rectangular Coordinates  163
3.9 Poisson's Equation: The Method of Eigenfunction Expansions  170
3.10 Neumann and Robin Conditions  180
3.11 The Maximum Principle  187
4  Partial Differential Equations in
Polar and Cylindrical Coordinates     193
4.1 The Laplacian in Various Coordinate Systems  194
4.2 Vibrations of a Circular Membrane: Symmetric Case  198
4.3 Vibrations of a Circular Membrane: General Case  207
4.4 Laplace's Equation in Circular Regions  216
4.5 Laplace's Equation in a Cylinder  228
4.6 The Helmholtz and Poisson Equations  231
Supplement on Bessel Functions
4.7 Bessel's Equation and Bessel Functions  237
4.8 Bessel Series Expansions  248
4.9 Integral Formulas and Asymptotics for Bessel Functions  261
5  Partial Differential Equations in Spherical Coordinates   269
5.1 Preview of Problems and Methods  270
5.2 Dirichlet Problems with Symmetry  274
5.3 Spherical Harmonics and the General Dirichlet Problem  281
5.4 The Helmholtz Equation with Applications to the P0isson, Heat,and Wave Equations  291
Supplement on Legendre Functions
5.5 Legendre's Differential Equation  300
5.6 Legendre Polynomials and Legendre Series Expansions  308
5.7 Associated Legendre Functions and Series Expansions  319
6  Sturm-Liouville Theory with Engineering Applications   325
6.1 Orthogonal Functions  326
6.2 Sturm-Liouville Theory  333
6.3 The Hanging Chain  346
6.4 Fourth Order Sturm-Liouville Theory  353
6.5 Elastic Vibrations and Buckling of Beams 360
6.6 The Biharmonic Operator  371
6.7 Vibrations of Circular Plates  377
7  The Fourier Transform and Its Applications    389
7.1 The Fourier Integral Representation  390
7.2 The Fourier Transform  398
7.3 The Fourier Transform Method  411
7.4 The Heat Equation and Gauss's Kernel  420
7.5 A Dirichlet Problem and the Poisson Integral Formula  429
7.6 The Fourier Cosine and Sine Transforms  433
7.7 Problems Involving Semi-Infinite Intervals  440
7.8 Generalized Functions  445
7.9 The Nonhomogeneous Heat Equation  461
7.10 Duhamel's Principle  471
8  The Laplace and Hankel Transforms with Applications   479
8.1 The Laplace Transform  480
8.2 Further Properties of the Laplace Transform  491
8.3 The Laplace Transform Method  502
8.4 The Hankel Transform with Applications  508
9  Finite Difference Numerical Methods     515
9.1 The Finite Difference Method for the Heat Equation  516
9.2 The Finite Difference Method for the Wave Equation  525
9.3 The Finite Difference Method for Laplace's Equation  533
9.4 Iteration Methods for Laplace's Equation  541
10  Sampling and Discrete Fourier Analysis with
Applications to Partial Differential Equations    546
10.1 The Sampling Theorem  547
10.2 Partial Differential Equations and the Sampling Theorem  555
10.3 The Discrete and Fast Fourier Transforms  559
10.4 The Fourier and Discrete Fourier Transforms  567
1 1  An Introduction to Quantum Mechanics    573
11.1 SchrSdinger's Equation  574
11.2 The Hydrogen Atom  581
11.3 Heisenberg's Uncertainty Principle  590
Supplement on Orthogonal Polynomials
11.4 Hermite and Laguerre Polynomials  597
12  Green's Functions and Conformal Mappings    611
12.1 Green's Theorem and Identities  612
12.2 Harmonic Functions and Green's Identities  622
12.3 Green's Functions  629
12.4 Green's Functions for the Disk and the Upper Half-Plane  638
12.5 Analytic Functions  645
12.6 Solving Dirichlet Problems with Conformal Mappings  663
12.7 Green's Functions and Conformal Mappings  674
12.8 Neumann Functions and the Solution of Neumann Problems  684
APPENDIXES
A  Ordinary Differential Equations:
Review of Concepts and Methods      A1
A.1 Linear Ordinary Differential Equations  A2
A.2 Linear Ordinary Differential Equations
with Constant Coefficients  Al0
A.3 Linear Ordinary Differential Equations
with Nonconstant Coefficients A21
A.4 The Power Series Method, Part I A28
A.5 The Power Series Method, Part II A40
A.6 The Method of Frobenius A51
B  Tables of Transforms
A65
B.1 Fourier Transforms  A66
B.2 Fourier Cosine Transforms  A68
B.3 Fourier Sine Transforms  A69
B.4 Laplace Transforms  A70
References       A73
Answers to Selected Exercises      A75
Index        A99

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