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Full Description
The last five years have seen an immense growth in the use of symbolic computing and mathematical software packages such as Maple. The first three chapters of this book provide a user-friendly introduction to computer-assisted algebra with Maple. The rest of the book then develops these techniques and demonstrates the use of this technology for deriving approximate solutions to differential equations (linear and nonlinear) and integrals. In each case, the mathematical concepts are comprehensively introduced, with an emphasis on understanding how solutions behave and why various approximations can be used. Where appropriate, the text integrates the use of Maple to extend the utility of traditional approximation techniques. Advanced Mathematical Methods with Maple is the ideal companion text for advanced undergraduate and graduate students of mathematics and the physical sciences. It incorporates over 1000 exercises with different levels of difficulty, for which solutions are provided on the Internet.
Contents
1. Introduction to Maple; 2. Simplification; 3. Functions and procedures; 4. Sequences, series and limits; 5. Asymptotic expansions; 6. Continued fractions and Pade approximants; 7. Linear equations and Green's functions; 8. Fourier series and systems of orthogonal functions; 9. Perturbation theory; 10. Sturm-Liouville systems; 11. Special functions; 12. Linear systems and Floquet theory; 13. Integrals and their approximation; 14. Stationary phase approximations; 15. Uniform approximations for differential equations; 16. Dynamical systems I; 17. Dynamical systems II: periodic orbits; 18. Discrete dynamical systems; 19. Periodically driven systems; Appendix I. The gamma and related functions; Appendix II. Elliptic functions; References; Index.
