**Metric Version – A First Course in Differential Equations with Modeling Applications 12th Edition, ISBN-13: 978-0357760192**

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- Publisher: ? Cengage Learning; 12th edition (June 12, 2023)
- Language: ? English
- 464 pages
- ISBN-10: ? 0357760190
- ISBN-13: ? 978-0357760192

Straightforward and easy to read, Zill’s * A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 12th EDITION,* gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications is supported by a bounty of pedagogical aids, including an abundance of examples, explanations, “Remarks” boxes, definitions and more.

**Table of Contents:**

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 Theory of 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 Differential Equations

8.1 Theory of 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

9.5 Second-Order Boundary-Value Problems

Chapter 9 In Review

Appendices

Appendix A: Integral-Defined Functions

Appendix B: Matrices

Appendix C: Laplace Transforms

Answers for Selected Odd-Numbered Problems

Index

* Dennis G. Zill,* Ph.D., received a doctorate in applied mathematics from Iowa State University and is a former professor of mathematics at Loyola Marymount University in Los Angeles, Loras College in Iowa and California Polytechnic State University. He is also the former chair of the mathematics department at Loyola Marymount University, where he currently holds the title of Professor Emeritus of Mathematics. Zill has interests in astronomy, modern literature, music, golf and good wine, while his research interests include special functions, differential equations, integral transformations and complex analysis.

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