• Extended homework problems at the end of selected section exercises were submitted and classroom-tested by members of the differential equations instructors.
• A new design helps students quickly identify resources in the text and emphasizes the application of differential equations in the world around them.
• The development of material in this text progresses intuitively, and explanations are clear and concise. Exercises reinforce and build on chapter content.
• The text guides students through material necessary to progress to the next level of study; its clear presentation and mathematical precision make it an excellent reference tool in future courses.
• While this text is time-tested and widely accepted, it has remained current with the addition of new exercises and the enhanced four-color presentation.
• Exercises in this edition have been updated to better test and challenge students.
• A new design helps students quickly identify resources in the text and emphasizes the application of differential equations in the world around them.

1. INTRODUCTION TO DIFFERENTIAL EQUATIONS.

Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review.

2. FIRST-ORDER DIFFERENTIAL EQUATIONS.

Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations and Integrating Factors. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review.

3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS.

Linear Models. Nonlinear Models. Modeling with Systems of First-Order Differential Equations. Chapter 3 in Review.

4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.

Preliminary Theory-Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients-Superposition Approach. Undetermined Coefficients-Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Differential Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review.

5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS.

Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review.

6. SERIES SOLUTIONS OF LINEAR EQUATIONS.

Review of Power Series Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review.

7. LAPLACE TRANSFORM.

Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review.

8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.

Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review.

9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.

Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. 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.

Dennis G. Zill, Loyola Marymount University

Dennis Zill received a PhD 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 a rank as Professor Emeritus of Mathematics. Zill holds interests in astronomy, modern literature, music, golf, and good wine, while his research interests include Special Functions, Differential Equations, Integral Transformations, and Complex Analysis.