A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 10th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, “Remarks” boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

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Half Title

Title

Statement

Copyright

Contents

Preface

Ch 1: Introduction to Differential Equations

Ch 1: Introduction

1.1: Definitions and Terminology

1.2: Initial-Value Problems

1.3: Differential Equations as Mathematical Models

Chapter 1 in Review

Ch 2: First-Order Differential Equations

Ch 2: Introduction

2.1: Solution Curves Without a Solution

2.2: Separable Equations

2.3: Linear Equations

2.4: Exact Equations

2.5: Solutions by Substitutions

2.6: A Numerical Method

Chapter 2 in Review

Ch 3: Modeling With First-Order Differential Equations

Ch 3: Introduction

3.1: Linear Models

3.2: Nonlinear Models

3.3: Modeling with Systems of First-Order DEs

Chapter 3 in Review

Ch 4: Higher-Order Differential Equations

Ch 4: Introduction

4.1: Preliminary Theory—Linear Equations

4.2: Reduction of Order

4.3: Homogeneous Linear Equations with Constant Coefficients

4.4: Undetermined Coefficients—Superposition Approach

4.5: Undetermined Coefficients—Annihilator Approach

4.6: Variation of Parameters

4.7: Cauchy-Euler Equation

4.8: Green’s Functions

4.9: Solving Systems of Linear DEs by Elimination

4.10: Nonlinear Differential Equations

Chapter 4 in Review

Ch 5: Modeling With Higher-Order Differential Equations

Ch 5: Introduction

5.1: Linear Models: Initial-Value Problems

5.2: Linear Models: Boundary-Value Problems

5.3 Nonlinear Models

Chapter 5 in Review

Ch 6: Series Solutions of Linear Equations

Ch 6: Introduction

6.1: Review of Power Series

6.2: Solutions About Ordinary Points

6.3: Solutions About Singular Points

6.4: Special Functions

Chapter 6 in Review

Ch 7: The Laplace Transform

Ch 7: Introduction

7.1: Definition of the Laplace Transform

7.2: Inverse Transforms and Transforms of Derivatives

7.3: Operational Properties I

7.4: Operational Properties II

7.5: The Dirac Delta Function

7.6: Systems of Linear Differential Equations

Chapter 7 in Review

Ch 8: Systems of Linear First-order Differential Equations

Ch 8: Introduction

8.1: Preliminary Theory—Linear Systems

8.2: Homogeneous Linear Systems

8.3: Nonhomogeneous Linear Systems

8.4: Matrix Exponential

Chapter 8 in Review

Ch 9: Numerical Solutions of Ordinary Differential Equations

Ch 9: Introduction

9.1: Euler Methods and Error Analysis

9.2: Runge-Kutta Methods

9.3: Multistep Methods

9.4: Higher-Order Equations and Systems

9.5: Second-Order Boundary-Value Problems

Chapter 9 in Review

Appendix I: Gamma Function

Appendix II: Matrices

Appendix III: Laplace Transforms

Answers for Selected Odd-Numbered Problems

Index

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