» Schaum's Outline of Advanced Calculus, Second Edition

Schaum's Outline of Advanced Calculus, Second Edition Reviews

Customer Rating:
Summary: Serious error in great book
Comment: The proof of Leibniz theorem on p.194 is completely wrong.
The proof uses the mean-value theorem for derivatives, not integrals, and needs uniform continuity to complete.
There are numerous typos, including the preface.

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Customer Rating:
Summary: Great reference for advanced calc/analysis
Comment: I have taken extensive coursework in undergraduate calculus, advanced calculus, and a 2-semester real analysis course with Rudin's 'principles.' This book was incredibly helpful to me, because it provides some examples of material that Rudin covers, and these examples helped me gain a better understanding of the material (there are 1370 solved problems!). There is nothing in this book about topology per se, but it does cover just about everything else: numbers, sequences, limits/continuity, derivatives, integrals, partial derivatives, vector geometry, multiple integrals, line integrals, infinite series/products, improper integrals, Fourier series & integrals, and gamma/beta functions. This book shines in the plethora of material covered, and because it focuses on solving difficult problems as opposed to routine ones. Another thing is that this book DOES include most of the answers to the supplementary problems - answers are only omitted, for example, when the question says to prove something (prove that the series converges, etc). My analysis professor *loved* improper integrals, so the chapter on that was especially helpful. This text also includes Dirichlet's test for series, which is left out of Rudin. There are a few minor typos that are easily spotted, but for $20 these mistakes can be overlooked. Overall a great reference with many helpful solved problems: A+

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Customer Rating:
Summary: It's working!
Comment: Son came home one weekend and announced he was failing his college calculus course. We purchased this book for him and he is now getting A's......to be honest though.....don't know for sure if it's the book or our threaat to terminate his weekly allowance if he failed.....think it's probably both.......and son says the book has helped.

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Customer Rating:
Summary: Lots of problems, no solutions
Comment: I don't know about you, but I buy Schaum books so I can have a large number of problems to work with answers so I know when I'm doing it right. My great frustration is people who say "don't look at the answers or you'll never learn the material". BS. That's fine for people with good highschool math preparation, but when you're striving to overcome the legacy of miserable math teachers in US public schools, it fails miserably. I can spend hours on a problem and still not get it. I think the problem for people like me is that we just don't know the language or know how to think about mathematics. Hence I'm giving the book 1 star. I'm looking for a supplement to an obtuse text for an advance calculus course, not another obtuse text.

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Customer Rating:
Summary: Ideal (solved examples) companion to your calculus textbook
Comment: If you are studying calculus, the books from Schaum will certainly help you to develop your problem solving ability.

This is NOT a real analysis textbook inspired on Bourbaki topology. So that some readers do not consider the material really advanced. I think they were expecting 18 ways to express the Axiom of Choice (Zorn Lemma for example) Godel conjecture, Fixed point theorems, path and non-path conected sets, differential forms, more terminology (homeomorphism, diffeomorphism, manifolds) etc...

The book has an approach similar to Piskunov or G.B. Thomas Junior books, that is, more elementary approaches (but note that elementary does not mean easy). Many solved problems.

Look at table of contents inside the book at amazon to grasp an idea of what you will get.

Overall, very good companion, practical and with many examples.

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