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科技人员用的高等数学方法PDF|Epub|txt|kindle电子书版本网盘下载

CarlM.Bender，StevenA.Orszag著著
出版社：世界图书出版公司北京公司
ISBN：9787506291910
出版时间：2008
标注页数：593页
文件大小：20MB
文件页数：608页
主题词：高等数学－数学方法－英文

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图书目录

PART Ⅰ FUNDAMENTALS3

1 Ordinary Differential Equations3

1.1 Ordinary Differential Equations3

1.2 Initial-Value and Boundary-Value Problems5

1.3 Theory of Homogeneous Linear Equations7

1.4 Solutions of Homogeneous Linear Equations11

1.5 Inhomogeneous Linear Equations14

1.6 First-Order Nonlinear Differential Equations20

1.7 Higher-Order Nonlinear Differential Equations24

1.8 Eigenvalue Problems27

1.9 Differential Equations in the Complex Plane29

Problems for CHAPTER130

2 Difference Equations36

2.1 The Calculus of Differences36

2.2 Elementary Difference Equations37

2.3 Homogeneous Linear Difference Equations40

2.4 Inhomogeneous Linear Difference Equations49

2.5 Nonlinear Difference Equations53

Problems for CHAPTER253

PART Ⅱ LOCAL ANALYSIS61

3 Approximate Solution of Linear Differential Equations61

3.1 Classification of Singular Points of Homogeneous Linear Equations62

3.2 Local Behavior Near Ordinary Points of Homogeneous Linear Equations66

3.3 Local Series Expansions About Regular Singular Points of Homogeneous Linear Equations68

3.4 Local Behavior at Irregular Singular Points of Homogeneous Linear Equations76

3.5 Irregular Singular Point at Infinity88

3.6 Local Analysis of Inhomogeneous Linear Equations103

3.7 Asymptotic Relations107

3.8 Asymptotic Series118

Problems for CHAPTER3136

4 Approximate Solution of Nonlinear Differential Equations146

4.1 Spontaneous Singularities146

4.2 Approximate Solutions of First-Order Nonlinear Differential Equations148

4.3 Approximate Solutions to Higher-Order Nonlinear Differential Equations152

4.4 Nonlinear Autonomous Systems171

4.5 Higher-Order Nonlinear Autonomous Systems185

Problems for CHAPTER4196

5 Approximate Solution of Difference Equations205

5.1 Introductory Comments205

5.2 Ordinary and Regular Singular Points of Linear Difference Equations206

5.3 Local Behavior Near an Irregular Singular Point at Infinity：Determination of Controlling Factors214

5.4 Asymptotic Behavior of n！as n→∞：The Stirling Series218

5.5 Local Behavior Near an Irregular Singular Point at Infinity：Full Asymptotic Series227

5.6 Local Behavior of Nonlinear Difference Equations233

Problems for CHAPTER5240

6 Asymptotic Expansion of Integrals247

6.1 Introduction247

6.2 Elementary Examples249

6.3 Integration by Parts252

6.4 Laplace’s Method and Watson’s Lemma261

6.5 Method of Stationary Phase276

6.6 Method of Steepest Descents280

6.7 Asymptotic Evaluation of Sums302

Problems for CHAPTER6306

PART Ⅲ PERTURBATION METHODS319

7 Perturbation Series319

7.1 Perturbation Theory319

7.2 Regular and Singular Perturbation Theory324

7.3 Perturbation Methods for Linear Eigenvalue Problems330

7.4 Asymptotic Matching335

7.5 Mathematical Structure of Perturbative Eigenvalue Problems350

Problems for CHAPTER7361

8 Summation of Series368

8.1 Improvement of Convergence368

8.2 Summation of Divergent Series379

8.3 Padé Summation383

8.4 Continued Fractions and Padé Approximants395

8.5 Convergence of Padé Approximants400

8.6 Padé Sequences for Stieltjes Functions405

Problems for CHAPTER8410

PART Ⅳ GLOBAL ANALYSIS417

9 Boundary Layer Theory417

9.1 Introduction to Boundary-Layer Theory419

9.2 Mathematical Structure of Boundary Layers：Inner，Outer，and Intermediate Limits426

9.3 Higher-Order Boundary Layer Theory431

9.4 Distinguished Limits and Boundary Layers of Thickness≠ε435

9.5 Miscellaneous Examples of Linear Boundary-Layer Problems446

9.6 Internal Boundary Layers455

9.7 Nonlinear Boundary-Layer Problems463

Problems for CHAPTER9479

10 WKB Theory484

10.1 The Exponential Approximation for Dissipative and Dispersive Phenomena484

10.2 Conditions for Validity of the WKB Approximation493

10.3 Patched Asymptotic Approximations：WKB Solution of Inhomogeneous Linear Equations497

10.4 Matched Asymptotic Approximations：Solution of the One-Turning-Point Problem504

10.5 Two-Turning-Point Problems：Eigenvalue Condition519

10.6 Tunneling524

10.7 Brief Discussion of Higher-Order WKB Approximations534

Problems for CHAPTER10539

11 Multiple-Scale Analysis544

11.1 Resonance and Secular Behavior544

11.2 Multiple-Scale Analysis549

11.3 Examples of Multiple-Scale Analysis551

11.4 The Mathieu Equation and Stability560

Problems for CHAPTER11566

Appendix—Useful Formulas569

References577

Index581