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Differential Equations with Mathematica, Fourth Edition is a supplementing reference which 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.
List of contents
1. Preface2. Introduction to Differential Equations3. First-Order Ordinary Differential Equations4. Applications of First-Order Ordinary Differential Equations5. Higher-Order Differential Equations6. Applications of Higher-Order Differential Equations7. Systems of Ordinary Differential Equations8. Applications of Systems of Ordinary Differential Equations9. Laplace Transform Methods10. Eigenvalue Problems and Fourier Series11. Partial Differential Equations12. Appendix: Getting Started13. The Mathematica Menu14. Bibliography15. Index
