书名：Introductory differential equations
责任者：Martha L. Abell | James P. Braselton.
ISBN\ISSN：9780124172197,0124172199
出版时间：2014
出版社：Academic Press,
分类号：数学
版次：Fourth edition.
前言
Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. The book provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies.
This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. It follows a traditional approach and includes ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide array of exercises ranging from straightforward to challenging. There are also new applications and extended projects made relevant to everyday life through the use of examples in a broad range of contexts.
This book will be of interest to undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering.
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目录
Preface vii
1. Introduction to Differential Equations
1.1. Introduction to Differential Equations: Vocabulary 3
Exercises 1.1 10
1.2. A Graphical Approach to Solutions: Slope Fields and Direction Fields 15
Exercises 1.2 19
Chapter 1 Summary: Essential Concepts and Formulas 22
Chapter 1 Review Exercises 23
2. First-Order Equations
2.1. Introduction to First-Order Equations 27
Exercises 2.1 32
2.2. Separable Equations 33
Exercises 2.2 39
2.3. First-Order Linear Equations 44
Exercises 2.3 49
2.4. Exact Differential Equations 53
Exercises 2.4 57
2.5. Substitution Methods and Special Equations 60
Exercises 2.5 64
2.6. Numerical Methods for First-Order Equations 69
Exercises 2.6 78
Chapter 2 Summary: Essential Concepts and Formulas 80
Chapter 2 Review Exercises 80
Differential Equations at Work 83
3. Applications of First-Order Differential Equations
3.1. Population Growth and Decay 89
Exercises 3.1 97
3.2. Newton's Law of Cooling and Related Problems 102
Exercises 3.2 107
3.3. Free-Falling Bodies 109
Exercises 3.3 115
Chapter 3 Summary: Essential Concepts and Formulas 118
Chapter 3 Review Exercises 119
Differential Equations at Work 124
4. Higher Order Equations
4.1. Second-Order Equations: An Introduction 132
Exercises 4.1 141
4.2. Solutions of Second-Order Linear Homogeneous Equations with Constant Coefficients 143 C3\Exercises 4.2 147
4.3. Solving Second-Order Linear Equations: Undetermined Coefficients 149
Exercises 4.3 155
4.4. Solving Second-Order Linear Equations: Variation of Parameters 158
Exercises 4.4 163
4.5. Solving Higher Order Linear Homogeneous Equations 166
Exercises 4.5 175
4.6. Solving Higher Order Linear Equations: Undetermined Coefficients and Variation of Parameters 179
Exercises 4.6 187
4.7. Cauchy-Euler Equations 189
Exercises 4.7 195
4.8. Power Series Solutions of Ordinary Differential Equations 197
Exercises 4.8 203
4.9. Series Solutions of Ordinary Differential Equations 206
Exercises 4.9 215
Chapter 4 Summary: Essential Concepts and Formulas 218
Chapter 4 Review Exercises 219
Differential Equations at Work 221
5. Applications of Higher Order Differential Equations
5.1. Simple Harmonic Motion 227
Exercises 5.1 232
5.2. Damped Motion 234
Exercises 5.2 241
5.3. Forced Motion 243
Exercises 5.3 249
5.4. Other Applications 252
Exercises 5.4 257
5.5. The Pendulum Problem 259
Exercises 5.5 262
Chapter 5 Summary: Essential Concepts and Formulas 265
Chapter 5 Review Exercises 265
Differential Equations at Work 269
6. Systems of Differential Equations
6.1. Introduction 277
Exercises 6.1 282
6.2. Review of Marix Algebra and Calculus 285
Exercises 6.2 293
6.3. An Introduction to Linear Systems 295
Exercises 6.3 301
6.4. First-Order Linear Homogeneous Systems with Constant Coefficients 304
Exercises 6.4 316
6.5. First-Order Linear Nonhomogeneous Systems: Undetermined Coefficients and Variation of Parameters 319
Exercises 6.5 325
6.6. Phase Portraits 329
Exercises 6.6 339
6.7. Nonlinear Systems 341
Exercises 6.7 345
6.8. Numerical Methods 350
Exercises 6.8 355
Chapter 6 Summary: Essential Concepts and Formulas 357
Chapter 6 Review Exercises 357
Differential Equations at Work 359
7. Applications of Systems of Ordinary Differential Equations
7.1. Mechanical and Electrical Problems with First-Order Linear Systems 365
Exercises 7.1 370
7.2. Diffsion and Population Problems with First-Oder Linear Systems 372
Exercises 7.2 378
7.3. Nonlinear Systems of Equations 380
Exercises 7.3 384
Chapter 7 Summary: Essential Concepts and Formulas 389
Chapter 7 Review Exercises 389
Differential Equations at Work 392
8. Introduction to the Laplace Transform
8.1. The Laplace Transform: Preliminary Definitions and Notation 400
Exercises 8.1 405
8.2. The Inverse Laplace Transform 407
Exercises 8.2 410
8.3. Solving Initial-Value Problems with the Laplace Transform 411
Exercises 8.3 414
8.4. Laplace Transforms of Several Important Functions 415
Exercises 8.4 424
8.5. The Convolution Theorem 427
Exercises 8.5 430
8.6. Laplace Transform Methods for Solving Systems 431
Exercises 8.6 434
8.7. Some Applications Using Laplace Transforms 435
Exercises 8.7 442
Chapter 8 Summary: Essential Concepts and Formulas 451
Chapter 8 Review Exercises 452
Differential Equations at Work 455
Answers to Selected Exercises 461
Bibliography 507
Appendices 509
Index 513
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