Introduction to Real Analysis (Hardcover)

~ John DePree (Author), Charles Swartz (Author)

Editorial Reviews

Product Description

Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations research, and engineering. The text presents the first elementary exposition of the gauge integral and offers a clear and thorough introduction to real numbers, developing topics in n-dimensions, and functions of several variables. Detailed treatments of Lagrange multipliers and the Kuhn-Tucker Theorem are also presented. The text concludes with coverage of important topics in abstract analysis, including the Stone-Weierstrass Theorem and the Banach Contraction Principle.

Product Details

• Hardcover: 355 pages
• Publisher: Wiley; Revised edition (June 14, 1988)
• Language: English
• ISBN-10: 0471853917
• ISBN-13: 978-0471853916
• Product Dimensions: 9.6 x 6.7 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #874,153 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

13 of 15 people found the following review helpful:

5.0 out of 5 stars A unique introductory book on real analysis, June 6, 2000

By	Pedro L. Ribeiro "lqp-man" (Cotia, SP Brazil) - See all my reviews (REAL NAME)

So, we have another book on introductory real analysis. Yes, But this one has its own shine, keeping it apart from the classics (Rudin, Apostol, Bartle): It contains the first (and maybe the only) elementary exposition of the marvellous gauge integral. It's a clever and surprising extension of the definition of the Riemann integral, made by Kurzweil and Henstock in the fifties, with the purpose of constructing a Riemann-type integral with all the properties of the Lebesgue integral, and recovering the original spirit of Newton and Leibiniz (as far as primitives are concerned). McShane later showed that this kind of integral totally supersedes the concept of Lebesgue integral and measure. The gauge integral also supersedes the improper and Stieljes integrals, with the big pedagogical advantages of the Riemann integral.

However, the book form presentations of this integral (given mainly by its creators) are incomprehensible, period. On the other hand, Depree/Swartz achieves the previously unfulfilled purpose of giving a human-readable presentation of the gauge integral. It uses it as the main tool for teaching integration, and this is great, because all the book is very readable and down-to-earth. This book has other pearls, like his great presentation of differentiation in several variables (done with Frechet and Gateaux derivatives in a very smooth and clear way, better than Lang), and good topological stuff concerned with analysis as needed. It develops a different way of thinking about analysis, and all you need is a little basic calculus.

All things concerned, it's a first-class book that deserves to be read more and more. Gauge integration is a unfairly forgotten tool, that can enlighten many unsolved problems in mathematics (constructive mathematical analysis) and physics (path integration, as seen for example in the Feynman-Kac formula, proven using gauge integration), or simply make people think about advanced integration and analysis in a simpler way.

1 of 3 people found the following review helpful:

5.0 out of 5 stars Correcting a mistake in my review..., June 12, 2000

By	Pedro L. Ribeiro "lqp-man" (Cotia, SP Brazil) - See all my reviews (REAL NAME)

In the place where it says that the Feynman-Kac formula is proven using gauge integration, please ignore it, because it's not true.