Solution Manual for A First Course in Differential Equations with Modeling Applications 11th Edition by Dennis G. Zill

Contents

Preface

Chapter 1: Introduction to Differential Equations

1.1 Definitions and Terminology

1.2 Initial-Value Problems

1.3 Differential Equations as Mathematical Models

Chapter 1 In Review

Chapter 2: First-Order Differential Equations

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

Chapter 3: Modeling with First-Order Differential Equations

3.1 Linear Models

3.2 Nonlinear Models

3.3 Modeling with Systems of First-Order DEs

Chapter 3 In Review

Chapter 4: Higher-Order Differential Equations

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 Equations

4.8 Green’s Functions

4.9 Solving Systems of Linear DEs by Elimination

4.10 Nonlinear Differential Equations

Chapter 4 In Review

Chapter 5: Modeling with Higher-Order Differential Equations

5.1 Linear Models: Initial-Value Problems

5.2 Linear Models: Boundary-Value Problems

5.3 Nonlinear Models

Chapter 5 In Review

Chapter 6: Series Solutions of Linear Equations

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

Chapter 7: The Laplace Transform

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

Chapter 8: Systems of Linear First-Order Differential Equations

8.1 Preliminary Theory – Linear Systems

8.2 Homogeneous Linear Systems

8.3 Nonhomogeneous Linear Systems

8.4 Matrix Exponential

Chapter 8 In Review

Chapter 9: Numerical Solutions of Ordinary Differential Equations

9.1 Euler Methods and Error Analysis

9.2 Runge-Kutta Methods

9.3 Multistep Methods

9.4 Higher-Order Equations and Systems

Chapter 9 In Review

Appendices

Appendix A: Integral-Defined Functions

Appendix B: Matrices

Appendix C: Laplace Transforms

Answers for Selected Odd-Numbered Problems

Index