Advanced Calculus, Third Edition 3rd Edition

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ISBN-13: 978-1577663027
ISBN-10: 1577663020
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Editorial Reviews

Review

"Buck's text is a classic and a gem of an advanced calculus text. In recent decades there has been a proliferation of Real Analysis/Advanced Calculus texts but Buck's text is unique in the combination of its perspicuity of exposition and the way it is able to communicate very abstract ideas in unusually concrete, computational, and intuitive terms. Its strength is its ability to deconstruct what are often presented as very abstract ideas in other texts while at the same time not oversimplifying the ideas. Its emphasis on computational examples and special cases (e.g., the implicit function theorem) makes for a much more natural transition for students who are used to thinking about analysis in computational terms from elementary calculus and differential equations, linear algebra, into the realms of advanced modern analysis. I've never seen a text that does this as well as Buck." --Steven Deckelman, University of Wisconsin, Stout

From the Publisher

Title of related interest from Waveland Press: Kirkwood, An Introduction to Analysis, Second Edition (ISBN 9781577662327).
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Product Details

  • Hardcover
  • Publisher: Waveland Pr Inc; 3 edition (January 1, 2003)
  • Language: English
  • ISBN-10: 1577663020
  • ISBN-13: 978-1577663027
  • Product Dimensions: 1.5 x 6.2 x 9 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #678,683 in Books (See Top 100 in Books)

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30 of 33 people found the following review helpful By Hasnor Lot on December 26, 2002
Format: Hardcover
The book under review is an easily accessible introduction to Advanced Calculus for those at the upper undergraduate level. As a student, I found it to be a successful mix of rigor and insight, a particularly valuable quality considering the fact that the subject is oftentimes the pons asinorum to abstract reasonings and proofs for most students of mathematics.
The book begins with a relatively "rigorous" refresher on the concepts of sets, functions, and graphs; later on a bunch of so-called field axioms are thrown in, but the author didn't treat these "basic concepts" extensively as interesting subjects in their own right. Some topological concepts are introduced next, then sequence, continuity, and differentiation; in that order. Up to the last item, the semester course was concluded. Notice that this was only page 125 of a 600 page book, hence my inability to comment on subsequent chapters following that elementary discussion of differentiation.
Pictures appropriate to the particular discussion are available; whenever possible the author attempted to provide a more intuitive understanding of a deep mathematical idea by discussing an example from the real world or through a physical interpretation.
The exercises vary in difficulty, but some are particularly hard that a solution manual would be very much welcomed. The hints and answers in the back are too brief to be of much use in demystifying those seemingly mysterious and unmotivated tricks needed in particular solution.
The author encourages the readers to employ any tool of elementary calculus learned earlier, an understandable choice since it was actually his decision not to introduce an axiomatic development of the subject that would compel the readers to deduce a solution to a problem from "scratch".
I would highly recommend the book, even for self-study to the mathematical enthusiasts. Those who desire a not-too-formidable introduction to real analysis may find this classic enjoyable.
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23 of 27 people found the following review helpful By A Customer on March 25, 2004
Format: Hardcover
This book provides a very readable and insightful account of the material that is usually covered in two semesters of advanced undergraduate courses usually called "Advanced Calculus" or "Real Analysis." Explanations are clear and concepts are well motivated. The problem sets are well-selected, and are do-able after reading the relevant chapters. This book is highly recommended for engineers or scientists wishing to gain a deeper understanding of mathematics, and for math majors preparing for graduate study in real analysis. It is a great book.
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13 of 14 people found the following review helpful By R. Reid on June 11, 2007
Format: Hardcover
The book was excellent, starting with the basics of sets and topology and building quickly to the traditional subjects of calculus. I particularly enjoyed the way the author was able to draw attention to the key ideas that come up again and again, the mean value theorem for example. I have never seen a better view of the foundation of calculus, and this book is never leaving my shelf.
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17 of 20 people found the following review helpful By "richbum" on August 17, 2001
Format: Hardcover
This book is extremely well written and comprehensive. It is appropriately approaches the subject and addresses the audience (primarily undergraduates) in an elegant manner with a fair amount of challenging problems, though never overestimates the reader's previous knowledge or background. Time and time again, I've found myself digging back in this book finding more depth and content through each pass. This is by far the best Advance Calculus book I've come across for undergraduates.
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8 of 9 people found the following review helpful By EMC2 on March 9, 2012
Format: Hardcover Verified Purchase
This book is one of the better written books on advanced calculus. The diagrams and figures are well done and specific to the examples or concepts being presented. However, this is not for a college student who is trying learn how to solve typical engineering problems. This is a theoretical math book of proofs and identifying limiting conditions, etc. The Exercise problems involve proving bounding characteristics of functions, showing where there is convergence or divergence, and discussing the "whys and hows" of non-specific surfaces or multiple integrals. You will not be reading about or solving problems involving rolling spheres, projectiles, fluids in motion, planetary motion or the conservation of energy. To paraphrase Jeff Foxworthy, "If you can solve the exercise problems based on what you read in the previous section, then you are probably a mathematician." It is still a very well written and organized book - but definitely for the theoretically minded student.
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4 of 4 people found the following review helpful By Luciano Santos on February 28, 2014
Format: Hardcover Verified Purchase
This book is a very good classic introduction to real analysis. It very clearly presents the usual sequence in one-variable analysis and does also good job with multivariable results. Concerning the great theorems of vector analysis (Green, Gauss, Stokes) it follows the classical approach but introduces differential forms without all the technical apparatus which is to be pursued further in books like Spivak's Calculus on Manifolds. The treatment is rigourous but it doesn't neglect computational and numerical aspects. Of course, I intend to proceed up to Rudin's "hard stone" after Buck. The new edition is a very attractive and not so expensive in comparison to other books on the subject.
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