图书介绍
A first course in differential equations with modeling applicationsPDF|Epub|txt|kindle电子书版本网盘下载
- Dennis G Zill 著
- 出版社： 世界图书出版公司
- ISBN：7506272431
- 出版时间：2004
- 标注页数：438页
- 文件大小：65MB
- 文件页数：508页
- 主题词：
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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