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Differential Equations with Mathematica, Fifth Edition uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica's diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica's built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, Mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica's outstanding graphics capabilities.
Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro where they have extensive experience instructing students at both the undergraduate and graduate levels. Other books by the authors include Differential Equations with Mathematica and Mathematica by Example.
1. Preface 2. Introduction to Differential Equations 3. First-Order Ordinary Differential Equations 4. Applications of First-Order Ordinary Differential Equations 5. Higher-Order Differential Equations 6. Applications of Higher-Order Differential Equations 7. Systems of Ordinary Differential Equations 8. Applications of Systems of Ordinary Differential Equations 9. Laplace Transform Methods 10. Eigenvalue Problems and Fourier Series 11. Partial Differential Equations 12. Appendix: Getting Started 13. The Mathematica Menu 14. Bibliography 15. Index
