A Friendly Introduction to Analysis [Paperback]

Witold A.J. Kosmala (Author)

Book Description

Publication Date: January 19, 2004 | ISBN-10: 0130457965 | ISBN-13: 978-0130457967 | Edition: 2nd

This book is designed to be an easily readable, intimidation-free guide to advanced calculus. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first book to cover both single and multivariable analysis in such a clear, reader-friendly setting. Chapter topics cover sequences, limits of functions, continuity, differentiation, integration, infinite series, sequences and series of functions, vector calculus, functions of two variables, and multiple integration. For individuals seeking math fun at a higher level.

Editorial Reviews

From the Back Cover

/*4579F-0, 0-13-045796-5, Kosmala, Witold J., Advanced Calculus: A Friendly Approach, 2/E*/ This book is designed to be an easily readable, intimidation-free guide to advanced calculus. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first book to cover both single and multivariable analysis in such a clear, reader-friendly setting. Chapter topics cover sequences, limits of functions, continuity, differentiation, integration, infinite series, sequences and series of functions, vector calculus, functions of two variables, and multiple integration. For individuals seeking math fun at a higher level.

Product Details

• Paperback: 600 pages
• Publisher: Prentice Hall; 2nd edition (January 19, 2004)
• Language: English
• ISBN-10: 0130457965
• ISBN-13: 978-0130457967
• Product Dimensions: 9.8 x 6.8 x 1 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 2.8 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #596,443 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

24 of 26 people found the following review helpful:

5.0 out of 5 stars Great book for learning, reference, and review., February 17, 2004

By 

"fprimex" - See all my reviews

This review is from: A Friendly Introduction to Analysis (Paperback)

The appeal this text has to readers is that it is approachable, readable, and thorough. Among the topics included are proof techniques, sequences, limits, and single and multi variable calculus.

In comparison to other books I have studied concerning this material, this text has been written with students making the transition from computational mathematics (calculus sequence, linear, DEs) to analytical, theorem proving mathematics in mind. There is a strong emphasis on conceptual understanding and on how the topics are related to one another, with motivation provided for the study of each topic. Theorems are presented in a logical sequence, a large number are proved, and the discussions are very useful in pointing out important aspects of theorems and special cases to consider.

Concerning exercises, one nice thing I have come to appreciate is that, while being an analysis text, computational exercises are provided to ensure that the concepts are fully understood. Following these exercises, the numerous examples will help when completing the requested proofs.

The second edition is noticeably slimmer than the first. This is mainly due to a change in typesetting (which is better, in my opinion; the text is closer together so the pages look more full). There was one chapter removed on Fourier Series, but this can now be downloaded from Dr. Kosmala's web site. Aside from this one removal, there is more material presented in the second edition to go along with the corrections and rearrangements to the first.

Analysis can be a difficult subject to grasp, so I highly recommend this text for (as the preface says) its "clarity, readability, and friendliness."

21 of 23 people found the following review helpful:

5.0 out of 5 stars Having problems with analysis? GET THIS BOOK!, October 25, 2004

By 

David H. Kwon (Philadelphia, PA) - See all my reviews
(REAL NAME)   

This review is from: A Friendly Introduction to Analysis (Paperback)

This is a wonderful book for all of you out there that are struggling with analysis because your professor has chosen a traditional analysis text that is very terse like Rudin. The problem with so many of the traditional analysis textbooks is that you need a professor by your side guiding you, and without that type of help a student beginning analysis would be completley lost.

So to remedy that situation I strongly recommend all of you future analysis students to first take a look at this book. I think one of the main problems with students taking analysis is that it overwhelms them at first because it is nothing like the rest of the undergraduate curriculum in school. The math programs at most universities ignore analysis until the senior year. Typically before that students are in math courses that are purely computational. Usually learning calculus out of Stewart or something and never really touching on the theoretical aspects of calculus.

So of course when a student hits analysis its going to be mind boggling. That is why this book is so wonderful. It is sort of bridge from computational calculus to advanced calculus. It is not intimidating like so many of the analysis books. It approaches each subject matter in a very clear fashion. It has many examples which is rare for an analysis book.

I found chapter 8 to be a wonderful treatment of sequences and series of functions. I think many students would agree that concepts such as uniform convergence can be confusing but the author does a great job illustrating this somewhat complex topic.

All I can say is I wish when I was taking analysis I had access to this book. I think this book is great for an undergraduate analysis class as well as a first year graduate level class.

I think also if you are doing self study to prepare for examinations I think this is a great reference book. I really appreciate the author's efforts to write an analysis textbook that is so easy to read.

5 of 5 people found the following review helpful:

1.0 out of 5 stars A big mistake, November 28, 2009

By 

RC "Math" (redlands, ca USA) - See all my reviews

This review is from: A Friendly Introduction to Analysis (Paperback)

I selected this text for my undergraduate analysis class. It was a big mistake
it starts out nice and chatty and "friendly" but the author soon buries the
material in detailed tangential remarks. Particularly annoying is
his comparing exercises to many previous ( and future!!) problems in
the text. Togetherbwith the remarks the text grinds to a halt trying
to leaf back and forth to reference them. My students found this book
to be very difficult. Even simple things to prove he sometimes refers
the reader to previous material. My students need help on simple
things involving series say. He includes so many different ratio tests
for example and then has few straightforward probs for them to do.
It was an ordeal selecting problemsfor them to do.
Many of the easy ones he refers them to previous probs in
the text so the student refers back to the earlier solution instead
of proving it himself. A really bad experience!