国外很好数学著作原版系列傅立叶级数和边值问题(第8版)(英文)

本书特色

[

1 Fourier series

Piecewise Continuous Functions

Fourier Cosine Series 4

Examples 6
1 Fourier series

Piecewise Continuous Functions

Fourier Cosine Series 4

Examples 6

Fourier Sine Series 9

Examples 10

Fourier Series 14

3 Partial Differential Equations of Physics

Linear Boundary Value Problems 60

One-Dimensional Heat Equation 62

Related Equations 65

Laplacian in Cylindrical and Spherical Coordinates 67

Derivations 70

Boundary Conditions 73

Duhamel’s Principle 75

A Vibrating String 80

Vibrations of Bars and Membranes 83

General Solution of a Wave Equation 87

Types of Equations and Boundary Conditions 92

4 The Fourier method

Linear Operators

Principle of Superposition 97

Examples 99

Eigenvalues and Eigenfunctions 102

A Temperature Problem 104

A Vibrating String Problem 107

Historical Development 111

5 Boundary value Problems

A Slab with Faces at Prescribed Temperatures 114

Related Temperature Problems 118

Temperatures in a Sphere 122

A Slab with Internally Generated Heat 125

Steady Temperatures in Rectangular Coordinates 131

Steady Temperatures in Cylindrical Coordinates 136

A String with Prescribed Initial Conditions 140

Resonance 146

An elastic Bar 149

Double fourier series 152

Periodic Boundary Conditions 155
Examples 16

Adaptations to Other Intervals 20

2 Convergence of Fourier Series

One-Sided Derivatives 25

A Property of Fourier Coefficients 28

Two Lemmas 31

A Fourier Theorem 35

A Related Fourier Theorem 38

Examples 39

Convergence on Other Intervals 43

A Lemma 47

Absolute and Uniform Convergence of Fourier Series 49

The Gibbs phenomenon 51

Differentiation of Fourier Series 54

Integration of Fourier Series 55
6 Fourier Integrals and Applications

The Fourier Integral Formula 161

Dirichlet’s Integral 163

Two Lemmas 165

A Fourier Integral Theorem 169

The Cosine and Sine Integrals 173

Some eigenvalue problems on Unbounded Intervals 174

More on Superposition of Solutions 177

Steady Temperatures in a Semi-Infinite Strip 179

Temperatures in a semi-Infinite Solid 182

Temperatures in an Unlimited Medium 187

7 Orthonormal sets

Inner Products and Orthonormal sets 189

Examples 191

Generalized Fourier Series 195

Examples 196

Best Approximation in the Mean 200

Bessel’s Inequality and Parseval,s Equation 203

Applications to Fourier Series 205

8 Sturm-Liouville Problems and Applications

Regular Sturm-Liouville Problems 210

Modifications 212

Orthogonal Eigenfunctions and Real Eigenvalues 213

Real-Valued Eigenfunctions 218

Nonnegative Eigenvalues 220

Methods of solution 221

Examples of Eigenfunction Expansions 227

A Temperature Problem in Rectangular Coordinates 234

Steady Temperatures 238

Other Coordinates 242

A Modification of the Method 245

Another modification 249

A Vertically Hung Elastic Bar 252
9 Bessel Functions and Applications

The Gamma Function 261

Bessel Functions Jv(x) 263

Solutions when v=0.1.2

Recurrence Relations 273

Bessel’s Integral Form 277

Some Consequences of the Integral Forms 279

The Zeros of Jn(x) 283

Zeros of related Functions 286

Orthogonal Sets of Bessel Functions 288

Proof of the Theorems 290

Two Lemmas 295

Fourier-Bessel Series 298

Examples 300

Temperatures in a Long Cylinder 305

A Temperature Problem in Shrunken Fittings 312

Internally Generated Heat 314

Temperatures in a Long Cylindrical Wedge 319

Vibration of a Circular Membrane 321

10 Legendre Polynomials and Applications

Solutions of Legendre’s Equation 326

Legendre Polynomials 328

Rodrigues’ Formula 333

Laplace’s Integral Form 336

Some Consequences of the Integral Form 338

Orthogonality of Legendre Polynomials 341

Normalized Legendre Polynomials 343

Legendre Series 345

The Eigenfunctions Pn(cos 8) 350

Dirichlet Problems in Spherical Regions 352

Steady Temperatures in a Hemisphere 356

11 Verification of Solutions and Uniqueness

Abel’s Test for Uniform Convergence 362

Verification of Solution of Temperature Problem 365

Uniqueness of Solutions of the Heat Equation 368

Verification of Solution of Vibrating String Problem 372

Uniqueness of Solutions of the Wave Equation 374

Appendixes

Bibliography 377

Some Fourier Series Expansions 381

Solutions of Some Regular Sturm-Liouville Problems 383

Some Fourier-Bessel Series Expansions 387

Index

编辑手记

]

内容简介

[

本书介绍了傅里叶级数及其在工程和物理学偏微分方程边值问题中的应用

]

封面

书名:国外很好数学著作原版系列傅立叶级数和边值问题(第8版)(英文)

作者:詹姆斯·沃德·布朗

页数:411

定价:¥48.0

出版社:哈尔滨工业大学出版社

出版日期:2018-06-01

ISBN:9787560381251

PDF电子书大小:158MB 高清扫描完整版