Elements of Real Analysis [Hardcover]

Herbert S. Gaskill (Author), Pallasena P. Narayanaswami (Author)

Book Description

Publication Date: September 5, 1997 | ISBN-10: 013897067X | ISBN-13: 978-0138970673 | Edition: 1st

Comprehensive in coverage, this book explores the principles of logic, the axioms for the real numbers, limits of sequences, limits of functions, differentiation and integration, infinite series, convergence, and uniform convergence for sequences of real-valued functions. Concepts are presented slowly and include the details of calculations as well as substantial explanations as to how and why one proceeds in the given manner. Uses the words WHY? and HOW? throughout; inviting readers to become active participants and to supply a missing argument or a simple calculation. Contains more than 1000 individual exercises. Stresses and reviews elementary algebra and symbol manipulation as essential tools for success at the kind of computations required in dealing with limiting processes.

Editorial Reviews

From the Back Cover

Comprehensive in coverage, this book explores the principles of logic, the axioms for the real numbers, limits of sequences, limits of functions, differentiation and integration, infinite series, convergence, and uniform convergence for sequences of real-valued functions. Concepts are presented slowly and include the details of calculations as well as substantial explanations as to how and why one proceeds in the given manner. Uses the words WHY? and HOW? throughout; inviting readers to become active participants and to supply a missing argument or a simple calculation. Contains more than 1000 individual exercises. Stresses and reviews elementary algebra and symbol manipulation as essential tools for success at the kind of computations required in dealing with limiting processes.

Product Details

• Hardcover: 501 pages
• Publisher: Prentice Hall; 1st edition (September 5, 1997)
• Language: English
• ISBN-10: 013897067X
• ISBN-13: 978-0138970673
• Product Dimensions: 9.2 x 7 x 1.3 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,519,178 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

5.0 out of 5 stars A Spoon-Feeding Book on Analysis, March 2, 2003

By A Customer

This review is from: Elements of Real Analysis (Hardcover)

This book is essentially the same book as the "Foundation of Analysis" by the same auther, which I used in an undergrad analysis class. I found it to be an outstanding book. A later analysis class used the baby Rudin, and I like Gaskill so much better. I dare say I did not learn anything new from the baby Rudin that I did not already know from Gaskill.

Some of the features I appreciate are (1) the plain language explanations of proofs and motivations before/after each theorem, and (2) graphs to illustrate the idea behind the theorems/examples. I wish other authors would include more graphs and illustrations!

If you want to understand the concepts behind how calculus works at Riemann level, this is a great book to start with. And I like Stromberg as a follow-up book. (There are some but not a lot of new things to learn even from Stromberg once you master Gaskill.)

However, this book does not mention analysis in R^n whereas the baby Rudin does. And the chapter on topology could be better in providing motivation and concrete examples. Things clicked for me when another book started out by saying that compactness can characterize a closed interval as versus an open interval in R.
And I would have like to see how this book would introduce Lebesgue measure. (Neither does the baby Rudin, but Stromberg does, and I appreciate learning something concrete like Lebesgue measure before abstract measure.)

1 of 3 people found the following review helpful:

5.0 out of 5 stars A good introduction to real analysis, September 24, 2002

By 

owen (NY United States) - See all my reviews

This review is from: Elements of Real Analysis (Hardcover)

The proofs of the book are clear and detail.