Introduction to Ordinary Differential Equations with Mathematica

A multimedia textbook package for a course in ordinary differential equations taught in a conventional lecture class or in a laboratory- based course. The multimedia package consists of a printed textbook, a cross-platform CD-ROM, plus ancillary materials delivered online through the world Web web. The textbook includes hundreds of exercises and worked examples, historical footnotes, rich use of graphics to aid in visualization of solutions, and extensive use of Mathemtiaca for symbolic and numerical techniques. A 400-page solutions manual is available for sites that adopt this package.

Inhalt

1. Basic Concepts.- 2. Using Mathematica.- 3. First-Order Differential Equations.- 4. The Package ODE • m.- 5. Existence and Uniqueness of Solutions of First-Order Differential Equations.- 6. Applications of First-Order Equations I.- 7. Applications of First-Order Equations II.- 8. Second-Order Linear Differential Equations.- 9. Second-Order Linear Differential Equations with Constant Coefficients.- 10. Using ODE to Solve Second-Order Linear Differential Equations.- 11.1 Mass-Spring Systems.- 12. Higher-Order Linear Differential Equations.- 13. Numerical Solutions of Differential Equations.- 14. The Laplace Transform.- 15. Systems of Linear Differential Equations.- 16. Phase Portraits of Linear Systems.- 17. Stability of Nonlinear Systems.- 18. Applications of Linear Systems.- 19. Applications of Nonlinear Systems.- 20 Power Series Solutions of Second-Order Equations.- 21. Frobenius Solutions of Second-Order Equations.- A. Appendix: Review of Linear Algebra and Matrix Theory.- A.l Vector and Matrix Notation.- A.2 Determinants and Inverses.- A.3 Systems of Linear Equations and Determinants.- A.4 Eigenvalues and Eigenvectors.- A.5 The Exponential of a Matrix.- A.6 Abstract Vector Spaces.- A.7 Vectors and Matrices with Mathematica.- A.8 Solving Equations with Mathematica.- A.9 Eigenvalues and Eigenvectors with Mathematica.- B. Appendix: Systems of Units.- Answers.- General Index.- Name Index.