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Advanced Calculus (Dover Books on Mathematics) Paperback – 1 Jul 1990

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Product details

  • Paperback: 544 pages
  • Publisher: Dover Publications Inc.; New edition edition (1 July 1990)
  • Language: English
  • ISBN-10: 0486661032
  • ISBN-13: 978-0486661032
  • Product Dimensions: 21.6 x 13.7 x 2.6 cm
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 45,674 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

22 of 26 people found the following review helpful By A Customer on 23 Jun. 1999
Format: Paperback
This book is amazing. It is one of the most excititng math texts I have ever studied out of. I encourage any math or physics undergrad to purchase a copy pronto. It is great for self-instruction, and it provides you a much more mature explanation compared to all the "dumbdowned" texts which are taught out of in most universities today. I can't wait to get done with this review so I can get back to it.
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2 of 2 people found the following review helpful By Yang Chen on 24 Nov. 2013
Format: Paperback Verified Purchase
As the topic, the author showed his excellent skill in derivation, and sometime I have to spend more time to proof myself one by one. The fist two chapters are very important, and I recommend one go through each step in detail.
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20 of 24 people found the following review helpful By A Customer on 10 April 1999
Format: Paperback
BEING FAMILIAR WITH MANY OTHER ADVANCED CALCULUS BOOKS, I STRONGLY RECOMMEND THIS ONE TO ANYONE WHO WANTS TO HAVE A DEEP UNDERSTANDING AND A SOLID FOUNDATION OF ANALYSIS.
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7 of 16 people found the following review helpful By CB on 20 Sept. 2009
Format: Paperback Verified Purchase
This book is not for the faint hearted, and is best regarded as a show-case for the author, rather than a study aid for the reader.

Anyone wanting to understand Advanced Calculus should read the Schaum Outline first, and then look at this book as an example of mathematical elegance.

Next stop - Harvard.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 20 reviews
106 of 108 people found the following review helpful
Suitable for certain Subjects 15 Aug. 2002
By Robert Heyward - Published on Amazon.com
Format: Paperback
I bought this textbook as a supplementary resource book for an advanced calculus class I once took although I ended up using it for a Differential Equations II class instead (in particular the partial differential equation and fourier series sections). This book does not present proofs as one might expect from many of today's Advanced Calculus classes. It does not present abstract theorems but rather applied Calculus and Differential Equations. You will not find logical connectives, quantifiers, techniques of proofs, set operations, induction, or completeness axioms in this book. What you will find is partial differentiation, line and surface integrals, definite integrals, fourier series, infinite series, etc. Electrical and Computer Engineers will find that they may benefit from the Vector, Fourier Series, and Laplace Transform chapters of this book. Physics majors are more likely to profit from the chapters on Partial Differentiation and Fourier Series.
Here's the textbooks chapter titles: 1) Partial Differentiation, 2) Vectors, 3) Differential Geometry', 4) Applications of Partial Differentation, 5) Stieltjes Integral, 6) Multiple Integrals, 7) Line and Surface Integrals, 8) Limits and Indeterminate Forms, 9) Infinite Series, 10) Convergence of Improper Integrals, 11) The Gamma Function. Evaluation of Definite Integrals, 12) Fourier Series, 13) The Laplace Transform, 14) Applications of the Laplace Transform.
The book may be considered as being written in the ole' school style. It was written by a former Professor of Mathematics at Harvard and was first printed in 1947. The relatively low cost of the textbook may be attributed to it not having been `updated' for a while, being devoid of any color, and being softbound. It has some worked out examples but focuses more on established theorems and lemmas to solve problems. The book is fairly well organized and is overall a good reference book.
49 of 51 people found the following review helpful
Old style Advanced Calculus 17 Aug. 2002
By G. Cantor - Published on Amazon.com
Format: Paperback
First of all, Mr. Heyward's review would be very difficult to improve upon. However, I would like to supplement his remarks by emphasizing that this text is a classic work ... albeit from a substantially different time and place. Despite the required Carbon dating, Dr. Widder does an excellent job overall and he introduces a format that many more modern books could profit from.
The last time I saw this text used in an Advanced Calculus course was in the early '70's. I was a grad student TA for the course and had to work with the material in detail. I found it to be clear, complete, and very useful ... especially for one interested in a more applied approach.
Every student of analysis should at least take a look at the book. The Dover edition is, as usual, very inexpensive ... another big plus.
21 of 24 people found the following review helpful
Lucid with good notation 5 Nov. 2000
By Ken Braithwaite - Published on Amazon.com
Format: Paperback
An excellent reference work, with some thoughtful choices of notation, which always helps. I thought the differential geometry sections were a bit thin, so if that is what you after look elsewhere. If you want a good book on the core of multi-variate calculus this one will serve you well. He proves everything, which is nice too.
15 of 17 people found the following review helpful
very interesting 25 Sept. 1999
By A Customer - Published on Amazon.com
Format: Paperback
Although I found a few typos, and a few pages could be clearer, I still think this is an excellent book. *Every* theorem is proven rigorously, with nice examples. A great reference to have. It will introduce you to advanced analysis and from there you can go on to real analysis and set theory.
14 of 17 people found the following review helpful
A bit of a hodge podge but still a useful reference 7 April 2003
By Edward H. Welbon - Published on Amazon.com
Format: Paperback
This text is very definitely written in the grand old non-geometrical style which some might find a bit more difficult to follow but the theory is sound with very good coverage of differentiation and integration including the essential elements of topology (it discusses compact sets without referring to them as such). My main complaint is that evidently in this era, it was stylish to omit certain details of the proofs. Other than that, it is still a serviceable text if used as a reference (especially considering the low price).
I feel fortunate to have inexpensively purchased my copy of this text and have no intention of selling it or my copy of "Elements of Calculus" by Granville, Smith and Longley. But I also feel fortunate that I didn't have to learn the subject from either text. One of the best part of buying a used math book is in the reading of the notations made by previous owners 8-)
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