Advanced Mathematical Methods with Maple

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Cambridge University Press, 2002 - Computers - 862 pages
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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.
 

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Contents

2
15
Simplification
63
4
67
7
74
8
82
Functions and procedures
91
Sequences series and limits
131
Asymptotic expansions
179
Special functions
377
Linear systems and Floquet theory
437
Integrals and their approximation
478
Stationary phase approximations
526
Uniform approximations for differential equations
573
Dynamical systems I
628
periodic orbits
673
Discrete Dynamical Systems
727

Continued fractions and Pade approximants
195
Linear differential equations and Greens functions
227
Fourier series and systems of orthogonal functions
267
Perturbation theory
301
SturmLiouville systems
342
Periodically driven systems
785
The gamma and related functions
834
References
845
Index
855
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About the author (2002)

D. Richards lives in the Napa valley, where she was born and raised. She has 3 children, 2 dogs, 1 cat and 1 big kid (the husband). All are an endless source of amusement and provide tons of material to write and laugh about.

She graduated from Vintage High School in 1988, then attended the first ever California State Summer School for the Arts, held at Loyola Marymount University. A few years later, she attended the Academy of Art college in San Francisco. With a year under her belt toward a degree in illustration, she went bravely into the working world with nothing more than a dream to someday be a real artist...and a good mom.

When Zeke hit the slopes... is the first book she has written, though Zeke has been around since the late 1980s when he was created in a a high scool art class (Thanks Mr. Gadberry!). Zeke has been on a few t-shirts and sweatshirts and cards, but never in a story...until now.

D. is planning on continuing Zeke's adventures and predicaments in other books soon to follow. Until then, she'll be practicing her boarding, to someday, be as good as Zeke.

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