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微分方程及边值问题 第3版 计算与模型【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

微分方程及边值问题 第3版 计算与模型
  • （美）爱德华兹，彭尼著 著
  • 出版社： 清华大学出版社
  • ISBN：7302099782
  • 出版时间：2004
  • 标注页数：787页
  • 文件大小：97MB
  • 文件页数：40082544页
  • 主题词：微分方程－教材－英文；边值问题－教材－英文

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图书目录

CHAPTER 1 First-Order Differential Equations1

1.1 Differential Equations and Mathematical Models1

1.2 Integrals as General and Particular Solutions10

1.3 Slope Fields and Solution Curves18

1.4 Separable Equations and Applications31

1.5 Linear First-Order Equations46

1.6 Substitution Methods and Exact Equations58

CHAPTER 2 Mathematical Models and Numerical Methods77

2.1 Population Models77

2.2 Equilibrium Solutions and Stability90

2.3 Acceleration-Velocity Models98

2.4 Numerical Approximation：Euler’s Method110

2.5 A CLoser Look at the Euler Method122

2.6 The Runge-Kutta Method132

CHAPTER 3 Linear Equations of Higher Order144

3.1 Introduction： Second-Order Linear Equations144

3.2 General Solutions of Linear Equations158

3.3 Homogeneous Equations with Constant Coefficients170

3.4 Mechanical Vibrations182

3.5 Nonhomogeneous Equations and Undetermined Coefficients195

3.6 Forced Oscillations and Resonance209

3.7 Electrical Circuits222

3.8 Endpoint Problems and Eigenvalues229

CHAPTER 4 Introduction to Systems of Differential Equations242

4.1 First-Order Systems and Applications242

4.2 The Method of Elimination254

4.3 Numerical Methods for Systems265

CHAPTER 5 Linear Systems of Differential Equations281

5.1 Matrices and Linear Systems281

5.2 The Eigenvalue Method for Homogeneous Systems300

5.3 Second-Order Systems and Mechanical Applications315

5.4 Multiple Eigenvalue Solutions328

5.5 Matrix Exponentials and Linear Systems344

5.6 Nonhomogeneous Linear Systems358

CHAPTER 6 Nonlinear Systems and Phenomena366

6.1 Stability and the Phase Plane366

6.2 Linear and Almost Linear Systems378

6.3 Ecological Models： Predators and Competitors393

6.4 Nonlinear Mechanical Systems406

6.5 Chaos in Dynamical Systems423

CHAPTER 7 Laplace Transform Methods435

7.1 Laplace Transforms and Inverse Transforms435

7.2 Transformation of Initial Value Problems446

7.3 Translation and Partial Fractions457

7.4 Derivatives， Integrals，and Products of Transforms467

7.5 Periodic and Piecewise Continuous Input Functions475

7.6 Impulses and Delta Functions486

CHAPTER 8 Power Series Methods497

8.1 Introduction and Review of Power Series497

8.2 Series Solutions Near Ordinary Points510

8.3 Regular Singular Points523

8.4 Method of Frobenius：The Exceptional Cases539

8.5 Bessel’s Equation554

8.6 Applications of Bessel Functions563

CHAPTER 9 Fourier Series Methods572

9.1 Periodic Functions and Trigonometric Series572

9.2 General Fourier Series and Convergence581

9.3 Fourier Sine and Cosine Series589

9.4 Applications of Fourier Series601

9.5 Heat Conduction and Separation of Variables606

9.6 Vibrating Strings and the One-Dimensional Wave Equation621

9.7 Steady-State Temperature and Laplace’s Equatiion635

CHAPTER 10 Eigenvalues and Boundary Value Problems645

10.1 Sturm-Liouville Problems and Eigenfunction Expansions645

10.2 Applications of Eigenfunction Series658

10.3 Steady Periodic Solutions and Natural Frequencies668

10.4 Cylindrical Coordinate Problems678

10.5 Higher-Dimensional Phenomena693

References for Further Study711

Appendix： Existence and Uniqueness of Solutions714

Answers to Selected Problems729

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