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. 

What's New

• In addition to new examples, figures and exposition, other new material includes an expanded table of Laplace transforms in Appendix C and a greater emphasis on the concepts of piecewise-linear differential equations and solutions that involve nonelementary integrals.

• Many exercise sets have been updated by the addition of new problems. Some of these problems involve new and interesting mathematical models.

• WebAssign: Zill's A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS continues to be fully supported by WebAssign. The powerful online learning, homework and course management system engages students in learning the math. WebAssign includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts, online learning tools like lecture videos and PowerPoint slides, plus robust course, section, assignment and question settings and online testing. WebAssign also has a differential equations boot camp, providing a review of important calculus prerequisite topics.

• The development of material in this text progresses intuitively and explanations are clear and concise. Exercises reinforce and build on chapter content.

• This 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 examples.

• In addition to new examples, figures and exposition, other new material includes an expanded table of Laplace transforms in Appendix C and a greater emphasis on the concepts of piecewise-linear differential equations and solutions that involve nonelementary integrals.

• Many exercise sets have been updated by the addition of new problems. Some of these problems involve new and interesting mathematical models.

• WebAssign: Zill's A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS continues to be fully supported by WebAssign. The powerful online learning, homework and course management system engages students in learning the math. WebAssign includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts, online learning tools like lecture videos and PowerPoint slides, plus robust course, section, assignment and question settings and online testing. WebAssign also has a differential equations boot camp, providing a review of important calculus prerequisite topics.

• The development of material in this text progresses intuitively and explanations are clear and concise. Exercises reinforce and build on chapter content.

• This 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 examples

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 Equations. Linear Equations. Exact Equations. 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 DEs. Chapter 3 in Review.

4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Theory of 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. Green's Functions. Solving Systems of Linear DEs 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. THE 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 DIFFERENTIAL EQUATIONS.
Theory of Linear Systems. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review.

9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.
Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review.

Appendix A: Integral-Defined Functions.
Appendix B: Matrices.
Appendix C: Table of Laplace Transforms.
Answers to Selected Odd-Numbered Problems.
Index. 

• Dennis G. Zill

  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.

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