A Course in Advanced Calculus (Dover Books on Mathematics) [Paperback]

Robert S. Borden (Author)

Book Description

Series: Dover Books on Mathematics | Publication Date: July 10, 1997

This excellent undergraduate calculus text offers students an unusual perspective on concepts of integration in Euclidean spaces and their relationship to other mathematical areas. Subjects include sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Preface. Problems. Problems with tips and solutions for some.

Product Details

• Paperback: 416 pages
• Publisher: Dover Publications (July 10, 1997)
• Language: English
• ISBN-10: 0486672905
• ISBN-13: 978-0486672908
• Product Dimensions: 8.4 x 5.4 x 0.8 inches
• Shipping Weight: 15.2 ounces (View shipping rates and policies)
• Average Customer Review: 3.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #1,334,432 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

3.0 out of 5 stars A few comments, August 5, 2005

By 

magellan (Santa Clara, CA) - See all my reviews
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This review is from: A Course in Advanced Calculus (Dover Books on Mathematics) (Paperback)

This book combines formal mathematical analysis with the usually more applied concepts in a first course in advanced calculus. However, I agree with the other comments here that the book is just too dense for the average student for a first course in these subjects. If you have a very good previous background in general analysis, or if you used Apostol's books for calculus in the past, you might find Borden's book accessible. I was mainly interested in a review of eigenvalues and vectors, but the concepts were still more technical than I was comfortable with, probably. So as a first book I would look elsewhere, unless you are very strong in mathematical analysis and are looking for a book that combines more formal topics there with advanced calculus topics. If it weren't for the inappropriately high level of difficulty, I would rate the book four or five stars just as a scholarly achievement, but a course in advanced calculus is still an undergraduate, not a graduate level class, and this book seems like it was intended for someone with a more advanced background.

5 of 6 people found the following review helpful:

4.0 out of 5 stars A Great Real Analysis Book with the Wrong Title, February 19, 2008

By 

William L. Koggenhop "Bill Kogg" (Detroit) - See all my reviews
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This review is from: A Course in Advanced Calculus (Dover Books on Mathematics) (Paperback)

Professor Borden writes with a very personable style. I find the concepts explained in a friendly, conversation like manner, with subject matter cadenced in a way that really doesn't leave the reader feeling lost. Borden provides very understandable examples to this subject, that I have previously found lacking in many other texts on the material in this book.

I have a Math & Comp Sci degree from a local Tech University, from some years ago. In that program during the 80's they usually didn't teach an Advanced Calculus class, however the topics contained in a more traditional A.C. class (such as the topics contained in David V. Widder's Advanced Calculus) were covered in other classes anyway (minus the Lebegue/Stieltjes Integrals). I can agree that for an undergraduate A.C. book with that scope, this would probably not be the right book.

This could be a Real Analysis book with the wrong title; if so, I think it's pretty darn good, with the way the subject matter is presented. Prior to reading Borden's book, I read Angus E. Taylor's General Theory of Functions and Integration. While the reviews just glow over this one, the level of Taylor's book was a bit over my head, certainly being geared for beginning graduate students probably the reason. Now by reading Bordens book and seeing the same material a second time, the subject matter is making much more sense, and explained in a more conversational manner certainly helps.

To some extent, Math books in the 80's were starting to be written in this style, at least for undergrads, by relaxing some of the stringency in the prose while retaining the rigor (or even lacking prose to begin with; apparently Rudin's book is supposed to be famous for that). For the material presented in Borden's book, this is probably the most accessible it can get, at least what I have found so far.

I rated this only four stars because I don't do the problems, so I can't judge that aspect of the text. I did hate it when the problems were out of sync with the text, so if that is true here, and this truly should not be an Advanced Calculus book, 4 stars it is.

6 of 9 people found the following review helpful:

2.0 out of 5 stars Too ambitious, January 14, 1999

By A Customer

This review is from: A Course in Advanced Calculus (Dover Books on Mathematics) (Paperback)

The author try's to cram an entire undergraduate course in Abstract algebra into the first 30 pages and the exercises are, by and large, much too difficult and have only a peripheral relationship to the text. Not suitable for a first course in advanced calculus.