Customer Reviews

Schaum's Outline of Advanced Calculus, Second Edition

5 star:		(10)
4 star:		(5)
3 star:		(2)
2 star:		(0)
1 star:		(3)

 

 

After finishing the first 3 semesters of what is basically applied Calculus, majors in pure mathematics part company with their fellow students and move on to what is called "advanced calculus" or "functional analysis". This jump to the next level of mathematics, in which basically students have to be taught calculus all over again from a rigorous proof-based method, is a rude awakening to many. Most textbooks used in this situation, such as those by Rudin, assume that a talented and enthusiastic instructor will be acting as tour guide for the student, and will fill in the gaps. Unfortunately, this is not always the case. This Schaum's outline works well for such a situation. It not only covers what you would expect to see in undergraduate analysis, it mixes proofs with solved numerical problems and applications so that the student does not get bogged down or bored as can be the case with many of the texts on the subject that have nothing but proofs as exercises. In that way, it is unconventional in its treatment of the subject. Also, it provides more explanation and tutorial than you will find in the average Schaum's outline, and is pretty good at illustrating the correct way to perform a proof. If you can afford it, an excellent companion text to this Schaum's outline is Abbott's "Understanding Analysis", which can be used for self teaching of analysis because it is so detailed and clear.

These books are a cheap suplement for courses or whatever you desire, and in general, especially the ones written by the late Murray Spiegel, are quite excellent.

These books are certainly not intended for courses as they cannot go into extreme depth. However, if they are assigned, the student is assumed to have enough sense to venture elsewhere (the library maybe) and find supplemental books for learning in depth stuff. Thats all part of learning.

This book (now in an updated version with some really weird title which makes it worth buying alone! ) is quite excellent. Don't go and get it expecting to learn a course from. But it is good for a) a supplement for a course. b) a supplement for another course... it has lots of solved problems which oftentimes help in other courses and c) to refresh yourself on things you may have forgotten.

I'd also recommend you get Spiegel's Mathematical Handbook. It is absolutely indespensible. It is just a fantastic thing that everyone should have. When you are born, they should cut your umbilical cord and hand you a copy of Spiegel's Mathematical Handbook and you will have no problems ever in life. Get both. Get a whole lot of Schaums because they are so damn cheap and useful.

I used this book during my undergraduate Mathematics program & quite frankly, it saved my skin. It cuts the fat & gets to the point. This is indispensible if you have to do a quick revision for tests or exams.

I really appreciated the "loads" of worked examples which greatly aided my understanding. It is best used as a *supplement* to other detailed books on the subject. It is still my prefered reference book on Advanced Calculus.

I bought this edition of schaum's ad calc to
replace my beloved but dog-eared first edition
(by Murray Spiegel alone).

Luckily I held onto the original because this
version is a disaster in terms of typos introduced -
especially in the sections on transforms.
On top of that, the publishers inexplicably
placed Murray Spiegel's name second (and even
out of alphabetical order!!) on the cover. This is
an unforgivable disrespect of scholarship and of
the memory of a terrific author who was
single-handedly responsible for most of the
original and excellent math texts from schaum's.

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.

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.

This book has great sentimental value for me! I love this book!!! It's got everything you need to get through multivariable calculus course and/or vector calculus & Fourier Series. It doesn't really go into any analysis stuff though; it's all concrete, so you can look at this to get the 'rough & ready' versions of theorems/proofs & then find the more rigorous & abstract versions somewhere else, or later on in your studies. It's also a good reference since it covers a lot more than what you might do in a course, & could be helpful for more than one course. It has so many solved problems & theorems that might not be done elsewhere. Get this if you're in maybe 2nd-year math & are going to carry on in math, science or engineering.

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+

Whilst as some reviewers have pointed out, the proofs offered are not always the most fundamental and rigorous available, this aspect of the text makes it surprisingly digestible. As an example, the last chapter (on complex variables) seems almost an afterthought. However the text in combination with the solved problems will have the reader performing integration using residues etc in no time. This area of calculus has many weighty tomes devoted to it, offering full and rigorous proofs of each theorem, but to gain a similar working facility to that described above one needs to trawl through almost an entire book, a much more time-consuming exercise. The book works similarly for many other areas of calculus. This I found very rewarding, as I was able to go from clueless to reasonably proficient at problem solving in a short time, which encouraged me to keep learning. The more advanced treatments are also much easier to digest once you have some familiarity and competence in the area.

The only real let-down are the typos, which seem to be more concentrated in some chapters rather than others, however they are generally easily spotted and accounted for.

The book is therefore perfect for scientists and engineers, as with a minimum of fuss it teaches the reader everything they need to know to perform calculations, and makes a good introductory text for aspiring mathematicians. At this price, you'd be crazy to not have it lying around somewhere.

I strongly recommed this book for any serious student who wants to master calculus. Most books dumb down concepts and are extremely expensive. This book gets straight to the point, has excellent worked out examples, and abundant rigorous problems. Most importantly it is very inexpensive. So throw away those glossy overpriced books with too many dumbed-down pictures. Get this one instead.