Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition

ISBN: 9781118531778

Designed for a first course in differential equations, the third edition of James R. Brannan and William E. Boyce’s Differential Equations: An Introduction to Modern Methods and Applications is consistent with the way engineers and scientists use mathematics in their daily work.
In this textbook, the authors emphasise a systems approach to the subject and integrate the use of modern computing technology in the context of contemporary applications from engineering and science. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems aims to prepare students in the course for the realities of the new millennium, providing the building blocks that help them become successful problem-solvers in today’s workplace.
Section exercises throughout the third edition provide hands-on experience in modeling, analysis, and computer experimentation. Projects at the end of each chapter are included to provide additional opportunities for students to explore the role played by differential equations in the sciences and engineering.


  • Presents more important results, theorems, and definitions in colored summary boxes to enable students to more easily review for tests and exams.
  • Some topics that appear only in exercises in the second edition will be included in the main text of the third. Important examples are the substitution methods for solving homogeneous equations and Bernoulli equations.
  • Numerical methods collected in a new, optional, chapter 8. The first three sections of this chapter will be accessible to students after Chapter 2.
  • Places more emphasis (via discussion, examples, and problems) on how models and applications depend on parameter values.
James R. Brannan
Clemson University

William E. Boyce
Rensselaer Polytechnic Institute

1. Introduction
2. First Order Differential Equations
3. Systems of Two First Order Equations
4. Second Order Linear Equations
5. The Laplace Transform
6. Systems of First Order Linear Equations
7. Nonlinear Differential Equations and Stability
8. Numerical Methods
9. Series Solutions of Second order Equations
10. Orthogonal Functions, Fourier Series and Boundary – Value Problems
11. Elementary Partial Differential Equations
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E-Text: 9781119042686
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Binder Version: 9781118981221
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Textbook: 9781118531778