Elementary differential equations and boundary value problems Eighth Edition【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

Elementary differential equations and boundary value problems Eighth EditionPDF格式电子书版下载

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Chapter 1 Introduction1

1.1 Some Basic Mathematical Models; Direction Fields1

1.2 Solutions of Some Differential Equations10

1.3 Classification of Differential Equations19

1.4 Historical Remarks26

Chapter 2 First Order Differential Equations31

2.1 Linear Equations; Method of Integrating Factors31

2.2 Separable Equations42

2.3 Modeling with First Order Equations50

2.4 Differences Between Linear and Nonlinear Equations68

2.5 Autonomous Equations and Population Dynamics78

2.6 Exact Equations and Integrating Factors94

2.7 Numerical Approximations: Euler's Method101

2.8 The Existence and Uniqueness Theorem110

2.9 First Order Difference Equations119

Chapter 3 Second Order Linear Equations135

3.1 Homogeneous Equations with Constant Coefficients135

3.2 Fundamental Solutions of Linear Homogeneous Equations143

3.3 Linear Independence and the Wronskian153

3.4 Complex Roots of the Characteristic Equation159

3.5 Repeated Roots; Reduction of Order166

3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients175

3.7 Variation of Parameters186

3.8 Mechanical and Electrical Vibrations192

3.9 Forced Vibrations207

Chapter 4 Higher Order Linear Equations219

4.1 General Theory of nth Order Linear Equations219

4.2 Homogeneous Equations with Constant Coefficients224

4.3 The Method of Undetermined Coefficients233

4.4 The Method of Variation of Parameters237

Chapter 5 Series Solutions of Second Order Linear Equations243

5.1 Review of Power Series243

5.2 Series Solutions Near an Ordinary Point, Part Ⅰ250

5.3 Series Solutions Near an Ordinary Point, Part Ⅱ261

5.4 Regular Singular Points268

5.5 Euler Equations273

5.6 Series Solutions Near a Regular Singular Point, Part Ⅰ279

5.7 Series Solutions Near a Regular Singular Point, Part Ⅱ286

5.8 Bessel's Equation294

Chapter 6 The Laplace Transform307

6.1 Definition of the Laplace Transform307

6.2 Solution of Initial Value Problems314

6.3 Step Functions325

6.4 Differential Equations with Discontinuous Forcing Functions332

6.5 Impulse Functions340

6.6 The Convolution Integral346

Chapter 7 Systems of First Order Linear Equations355

7.1 Introduction355

7.2 Review of Matrices364

7.3 Linear Algebraic Equations; Linear Independence, Eigenvalues,Eigenvectors374

7.4 Basic Theory of Systems of First Order Linear Equations385

7.5 Homogeneous Linear Systems with Constant Coefficients390

7.6 Complex Eigenvalues401

7.7 Fundamental Matrices414

7.8 Repeated Eigenvalues422

7.9 Nonhomogeneous Linear Systems431

Chapter 8 Numerical Methods441

8.1 The Euler or Tangent Line Method441

8.2 Improvements on the Euler Method452

8.3 The Runge-Kutta Method457

8.4 Multistep Methods462

8.5 More on Errors; Stability468

8.6 Systems of First Order Equations478

Chapter 9 Nonlinear Differential Equations and Stability483

9.1 The Phase Plane: Linear Systems483

9.2 Autonomous Systems and Stability495

9.3 Almost Linear Systems503

9.4 Competing Species515

9.5 Predator-Prey Equations528

9.6 Liapunov's Second Method536

9.7 Periodic Solutions and Limit Cycles547

9.8 Chaos and Strange Attractors: The Lorenz Equations558

Chapter 10 Partial Differential Equations and Fourier Series569

10.1 Two-Point Boundary Value Problems569

10.2 Fourier Series576

10.3 The Fourier Convergence Theorem587

10.4 Even and Odd Functions594

10.5 Separation of Variables; Heat Conduction in a Rod603

10.6 Other Heat Conduction Problems612

10.7 The Wave Equation: Vibrations of an Elastic String623

10.8 Laplace's Equation638

Appendix A Derivation of the Heat Conduction Equation649

Appendix B Derivation of the Wave Equation653

Chapter 11 Boundary Value Problems657

11.1 The Occurrence of Two-Point Boundary Value Problems657

11.2 Sturm-Liouville Boundary Value Problems665

11.3 Nonhomogeneous Boundary Value Problems679

11.4 Singular Sturm-Liouville Problems695

11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion702

11.6 Series of Orthogonal Functions: Mean Convergence709

Answers to Problems719

Index781