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Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles

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$99.00
Order Code:
OT139

 Product Description

by John P. Boyd

-

2014 / xviii + 460 / softcover / ISBN 978-1-611973-51-8 / List Price $99.00 / Member Price $69.30 / Order Code OT139

Keywords: rootfinding, Chebyshev polynomials, transcendental equations, nonlinear algebra, Chebyshev Proxy Rootfinder (CPR)

Contents
Preface
Index
SIREV Book Review


Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute— not always needed, but indispensible when it is. The author’s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations.

Solving Transcendental Equations is unique in that it

  • is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding.
  • includes three chapters on analytical methods—explicit solutions, regular perturbation expansions, and singular perturbation series (including hyperasymptotics)—unlike other books that give only numerical algorithms for solving algebraic and transcendental equations.

Audience
This book is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes and as a reference for engineers and others working with difficult equations.

About the Author
John P. Boyd joined the faculty at the University of Michigan in 1977 and has been professor of atmospheric, oceanic, and space science in the College of Engineering since 1988. Concurrently, he was the founding associate director of the Laboratory for Scientific Computation (now the Michigan Institute for Computational Discovery and Engineering) and as such created the university's M. S. and Ph.D. degrees in scientific computing. His previous books are Chebyshev and Fourier Spectral Methods, 2nd edition, Dover, 2001) and Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics (Springer, 1998). He has also published 240 journal articles in atmospheric and oceanic dynamics, nonlinear waves, physics, and Chebyshev, Fourier, and RBF spectral methods, as well as 20 science fiction stories.

ISBN 9781611973518

Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute— not always needed, but indispensible when it is. The author’s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations.

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