Practical Analysis in One Variable | 
 enlarge | Author: Donald Estep
Publisher: Springer
Category: Book
List Price: $69.95
Buy New: $52.11
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Rating:  1 reviews
Sales Rank: 1564966
Media: Hardcover
Edition: 1
Pages: 648
Number Of Items: 1
Shipping Weight (lbs): 2.3
Dimensions (in): 9 x 6.8 x 1.3
ISBN: 0387954848
Dewey Decimal Number: 515
EAN: 9780387954844
Publication Date: October 1, 2002
Availability: Usually ships in 1-2 business days
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Product Description
This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. The book can be used in an honor calculus sequence typically taken by freshmen planning to major in engineering, mathematics, and science, or in an introductory course in rigorous real analysis offered to mathematics majors. Donald Estep is Professor of Mathematics at Colorado State University. He is the author of Computational Differential Equations, with K. Eriksson, P. Hansbo and C. Johnson (Cambridge University Press 1996) and Error of Numerical Solutions of Systems of Nonlinear Reaction-Diffusion Equations with M. Larson and R. Williams (A.M.S. 2000), and recently co-edited Collected Lectures on the Preservation of Stability under Discretization, with Simon Tavener (S.I.A.M., 2002), as well as numerous research articles. His research interests include computational error estimation and adaptive finite element methods, numerical solution of evolutionary problems, and computational investigation of physical models.
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| Customer Reviews:
Finally, the context of analysis laid bare June 8, 2006
Jeffrey D. Younger
4 out of 4 found this review helpful
Students of analysis are often beset with frustration. They ask "Why did you bound that quantity with that other quantity?" The typical answer, "Because it works out in the proof!" is certainly true, yet wholly unsatisfactory for the student.
This book begins with models, real-world problems, that originally motivated the development of analysis. The student easily grasps how, and more importantly why, quantities are bounded. The days of staring at an algebraic form for hours are gone! (Well, mostly.)
Instead of the normal calculus-style, simple-to-complex development of the material, Estep introduces concepts in the natural order of the real-world problems. For example, Lipschitz continuity is introduced early to solve obvious extensions to previous problems. The mathematical idea of continuity is progressively extended and provides much of the motivation for the second half of the book.
By orienting on the problems solved by analysis, Estep avoids many of the bewildering difficulties encountered in traditional introductory treatments. This is the best introductory analysis book I've seen. I'm very surprised that it hasn't received more attention.
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