Preface | p. ix |

Acknowledgments | p. xv |

Introduction to Differential Equations | p. 1 |

Definitions and Terminology | p. 2 |

Initial-Value Problems | p. 15 |

Differential Equations as Mathematical Models | p. 22 |

Chapter 1 in Review | p. 37 |

First-Order Differential Equations | p. 39 |

Solution Curves Without the Solution | p. 40 |

Separable Variables | p. 51 |

Linear Equations | p. 60 |

Exact Equations | p. 72 |

Solutions by Substitutions | p. 80 |

A Numerical Solution | p. 86 |

Chapter 2 in Review | p. 92 |

Modeling with First-Order Differential Equations | p. 95 |

Linear Equations | p. 96 |

Nonlinear Equations | p. 109 |

Systems of Linear and Nonlinear Differential Equations | p. 121 |

Chapter 3 in Review | p. 130 |

Project Module: Harvesting of Renewable Natural Resources | p. 133 |

Higher-Order Differential Equations | p. 138 |

Preliminary Theory: Linear Equations | p. 139 |

Initial-Value and Boundary-Value Problems | p. 139 |

Homogeneous Equations | p. 142 |

Nonhomogeneous Equations | p. 148 |

Reduction of Order | p. 154 |

Homogeneous Linear Equations with Constant Coefficients | p. 158 |

Undetermined Coefficients--Superposition Approach | p. 167 |

Undetermined Coefficients--Annihilator Approach | p. 178 |

Variation of Parameters | p. 188 |

Cauchy-Euler Equation | p. 193 |

Solving Systems of Linear Equations by Elimination | p. 201 |

Nonlinear Equations | p. 207 |

Chapter 4 in Review | p. 212 |

Modeling with Higher-Order Differential Equations | p. 215 |

Linear Equations: Initial-Value Problems | p. 216 |

Spring/Mass Systems: Free Undamped Motion | p. 216 |

Spring/Mass Systems: Free Damped Motion | p. 220 |

Spring/Mass Systems: Driven Motion | p. 224 |

Series Circuit Analogue | p. 227 |

Linear Equations: Boundary-Value Problems | p. 237 |

Nonlinear Equations | p. 247 |

Chapter 5 in Review | p. 259 |

Project Module: The Collapse of the Tacoma Narrows Suspension Bridge | p. 263 |

Series Solutions of Linear Equations | p. 267 |

Solutions About Ordinary Points | p. 268 |

Review of Power Series | p. 268 |

Power Series Solutions | p. 271 |

Solutions About Singular Points | p. 280 |

Two Special Equations | p. 292 |

Chapter 6 in Review | p. 304 |

The Laplace Transform | p. 306 |

Definition of the Laplace Transform | p. 307 |

Inverse Transform and Transforms of Derivatives | p. 314 |

Translation Theorems | p. 324 |

Translation on the s-Axis | p. 324 |

Translation on the t-Axis | p. 328 |

Additional Operational Properties | p. 338 |

Dirac Delta Function | p. 351 |

Systems of Linear Equations | p. 354 |

Chapter 7 in Review | p. 361 |

Systems of Linear First-Order Differential Equations | p. 364 |

Preliminary Theory | p. 365 |

Homogeneous Linear Systems with Constant Coefficients | p. 375 |

Distinct Real Eigenvalues | p. 376 |

Repeated Eigenvalues | p. 380 |

Complex Eigenvalues | p. 384 |

Variation of Parameters | p. 393 |

Matrix Exponential | p. 399 |

Chapter 8 in Review | p. 404 |

Project Module: Earthquake Shaking of Multistory Buildings | p. 406 |

Numerical Solutions of Ordinary Differential Equations | p. 410 |

Euler Methods and Error Analysis | p. 411 |

Runge-Kutta Methods | p. 417 |

Multistep Methods | p. 424 |

Higher-Order Equations and Systems | p. 427 |

Second-Order Boundary-Value Problems | p. 433 |

Chapter 9 in Review | p. 438 |

Appendixes | p. 1 |

Gamma Functions | p. 1 |

Introduction to Matrices | p. 3 |

Laplace Transforms | p. 25 |

Selected Answers for Odd-Numbered Problems | p. 1 |

Index | p. 1 |

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