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微分方程与边界值问题 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）兹尔（Zill，D.G.） （美）库伦（Cullen，M.R.）著 著
- 出版社： 北京：机械工业出版社
- ISBN：7111123182
- 出版时间：2003
- 标注页数：631页
- 文件大小：41MB
- 文件页数：721页
- 主题词：微分方程－高等学校－教材－英文；边值问题－高等学校－教材－英文
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图书目录
1 INTRODUCTION TO DIFFERENTIAL EQUATIONS1
1.1 Definitions and Terminology2
1.2 Initial-Value Problems15
1.3 Differential Equations as Mathematical Models22
Chapter 1 in Review37
2 FIRST-ORDER DIFFERENTIAL EQUATIONS39
2.1 Solution Curves Without the Solution40
2.2 Separable Variables51
2.3 Linear Equations60
2.4 Exact Equations72
2.5 Solutions by Substitutions80
2.6 A Numerical Solution86
Chapter 2 in Review92
3 MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS95
3.1 Linear Equations96
3.2 Nonlinear Equations109
3.3 Systems of Linear and Nonlinear Differential Equations121
Chapter 3 in Review130
Project Module: Harvesting of Renewable Natural Resources, by Gilbert N. Lewis133
4 HIGHER-ORDER DIFFERENTIAL EQUATIONS138
4.1 Preliminary Theory: Linear Equations139
4.1.1 Initial-Value and Boundary-Value Problems139
4.1.2 Homogeneous Equations142
4.1.3 Nonhomogeneous Equations148
4.2 Reduction of Order154
4.3 Homogeneous Linear Equations with Constant Coefficients158
4.4 Undetermined Coefficients—Superposition Approach167
4.5 Undetermined Coefficients—Annihilator Approach178
4.6 Variation of Parameters188
4.7 Cauchy-Euler Equation193
4.8 Solving Systems of Linear Equations by Elimination201
4.9 Nonlinear Equations207
Chapter 4 in Review212
5 MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS215
5.1 Linear Equations: Initial-Value Problems216
5.1.1 Spring/Mass Systems: Free Undamped Motion216
5.1.2 Spring/Mass Systems: Free Damped Motion220
5.1.3 Spring/Mass Systems: Driven Motion224
5.1.4 Series Circuit Analogue227
5.2 Linear Equations: Boundary-Value Problems237
5.3 Nonlinear Equations247
Chapter 5 in Review259
Project Module: The Collapse of the Tacoma Narrows Suspension Bridge, by Gilbert N. Lewis263
6 SERIES SOLUTIONS Of LINEAR EQUATIONS267
6.1 Solutions About Ordinary Points268
6.1.1 Review of Power Series268
6.1.2 Power Series Solutions271
6.2 Solutions About Singular Points280
6.3 Two Special Equations292
Chapter 6 in Review304
7 THE LAPLACE TRANSFORM306
7.1 Definition of the Laplace Transform307
7.2 Inverse Transform and Transforms of Derivatives314
7.3 Translation Theorems324
7.3.1 Translation on the s-Axis324
7.3.2 Translation on the t-Axis328
7.4 Additional Operational Properties338
7.5 Dirac Delta Function351
7.6 Systems of Linear Equations354
Chapter 7 in Review361
8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS364
8.1 Preliminary Theory365
8.2 Homogeneous Linear Systems with Constant Coefficients375
8.2.1 Distinct Real Eigenvalues376
8.2.2 Repeated Eigenvalues380
8.2.3 Complex Eigenvalues384
8.3 Variation of Parameters393
8.4 Matrix Exponential399
Chapter 8 in Review404
Project Module: Earthquake Shaking of Multistory Buildings, by Gilbert N. Lewis406
9 NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS410
9.1 Euler Methods and Error Analysis411
9.2 Runge-Kutta Methods417
9.3 Multistep Methods424
9.4 Higher-Order Equations and Systems427
9.5 Second-Order Boundary-Value Problems433
Chapter 9 in Review438
10 PLANE AUTONOMOUS SYSTEMS AND STABILITY439
10.1 Autonomous Systems, Critical Points, and Periodic Solutions440
10.2 Stability of Linear Systems448
10.3 Linearization and Local Stability458
10.4 Modeling Using Autonomous Systems470
Chapter 10 in Review480
11 ORTHOGONAL FUNCTIONS AND FOURIER SERIES483
11.1 Orthogonal Functions484
11.2 Fourier Series489
11.3 Fourier Cosine and Sine Series495
11.4 Sturm-Liouville Problem504
11.5 Bessel and Legendre Series511
11.5.1 Fourier-Bessel Series512
11.5.2 Fourier-Legendre Series515
Chapter 11 in Review519
12 PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES521
12.1 Separable Partial Differential Equations522
12.2 Classical Equations and Boundary-Value Problems527
12.3 Heat Equation533
12.4 Wave Equation536
12.5 Laplace s Equation542
12.6 Nonhomogeneous Equations and Boundary Conditions547
12.7 Orthogonal Series Expansions551
12.8 Boundary-Value Problems Involving Fourier Series in Two Variables555
Chapter 12 in Review559
13 BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS561
13.1 Problems Involving Laplace s Equation in Polar Coordinates562
13.2 Problems in Polar and Cylindrical Coordinates: Bessel Functions567
13.3 Problems in Spherical Coordinates: Legendre Polynomials575
Chapter 13 in Review578
14 INTEGRAL TRANSFORM METHOD581
14.1 Error Function582
14.2 Applications of the Laplace Transform584
14.3 Fourier Integral595
14.4 Fourier Transforms601
Chapter 14 in Review607
15 NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS610
15.1 Elliptic Equations611
15.2 Parabolic Equations617
15.3 Hyperbolic Equations625
Chapter 15 in Review630