Calculus, Multi-Variable Calculus and Linear Algebra with Applications (Calculus)

Rating:
Summary: Weak
Review: Few books in the mathematical literature have given me so much pain as this one. Freshman year, I took a heavily theoretical linear algebra class with Tommy II as the textbook, and then the next term I took multivariable calculus out of this book as well. In either case, this book was my first experience with the material, though as an "introductory" text it should have done the job. Suffice it to say that neither experience was terribly positive.

My problem is that Apostol never seems to try to motivate ideas well, and he uses cumbersome, nonstandard, and occasionally inconsistent notation. His proofs can be inelegant and opaque at times. He is far too sparing on geometrical intuition as a way to understand the material, preferring to talk in symbols rather than pictures. (This is especially true in the first five chapters on linear algebra. His multivariable chapters are well-illustrated, but calculus on R^n seems to be trivial once calculus on R is under your belt from a good introductory book like Larson/Hostetler/Edwards at a high-school pace. Thus, the motivation is needed least where it is used most.) As a result, I feel that I still don't intuitively understand how operators work on inner-product spaces, even after trying to remedy my deficiencies for a year and a half now.

I attributed my lack of understanding to my stupidity, but then I found myself learning exterior forms from Arnol'd's excellent mathematical mechanics book and groups from Dummit/Foote's superb abstract algebra text - and understanding the exposition perfectly. And I started to feel that this book is the thing at fault.

If a prospective reader is prepared for the terseness and difficulty of Apostol, I recommend that s/he go straight to the real math rather than settling for this obfuscated treatment of inroductory subjects. It is no harder to learn the rudiments of metric topology than it is to learn Apostol's open balls, and it seems no more inspired to take on Halmos' linear algebra classic, with its intimations of Hilbert space, than it is to struggle through Apostol's treatment. (The former seems to combine considerable difficulty with terse, but wonderful, motivation, but don't take my work on that: I'm only forty pages into it!) But the books are more inspired, and the math is far more general and beautiful.

My recommendation: learn your calculus (and potentially your first linear algebra) patiently but thoroughly from a prosaic, worked-example-ridden, 1000-page monster, then go straight to the upper undergraduate/early graduate classics for the real fun. Tommy II, caught somewhere in the middle, has no place in this plan.

Rating:
Summary: Review of Tommy Volume 2
Review: I am currently enrolled in BC Calculus in my high school as well as linear algebra at a local college. What better way to learn both together than with Tommy. This is a great book to learn the connections between the two and how to do real linear algebra, not straight algebra but differentiating and doing calculus on whatever spaces you want. It's very concise, however not so clear. I skipped into BC and spend a lot of free time doing math and this book is still a bit deep. Also, the tie-ins to LA are definitely not going to be apparent off the bat. I have a really great LA teacher so I find myself skipping over some of his more complicated expressions of very simple items, however if i were a newcomer to LA, this would be totally confusing and Greek. I agree with the other reviewers, if you're familiar with calculus and LA and want to learn more about each and their connections, this is the bible, however, if you're a newcomer to one or both, definitely learn each separately and more simply. The book is very proof based and states it assumes you know how to use the mathematical objects it's presenting, now it's showing you why they work. Some of his expressions are like physics problems mindset, first look you'll have no idea, but if you think about it, eventually the ideas all fall together. A great book and recomended to anyone experienced enough to handle it.

Rating:
Summary: substance w/o the frills
Review: I was looking for a solid reference book and was quite fortunate to stumble across Apostol's two texts. His writing is clear and concise. What I appreciate most is his axiomatic approach. He builds up everything as opposed to the numerous calculus cookbooks out there. Every theorem has a proof.

Rating:
Summary: substance w/o the frills
Review: I was looking for a solid reference book and was quite fortunate to stumble across Apostol's two texts. His writing is clear and concise. What I appreciate most is his axiomatic approach. He builds up everything as opposed to the numerous calculus cookbooks out there. Every theorem has a proof.

Rating:
Summary: Very thorough, but very dense
Review: I'm currently taking an honors calculus sequence at the U of WI, and have used this book and the first volume for the past three semesters. Needless to say, you have to take Apostol with a grain of salt. Although the no-frills style and lack of worked examples is upsetting to many students who are used to pictures, thorough examples, and color, these volumes cover a lot of material in a small space. And also beware; my professor and others in the math department have found errors in definitions and theorems, and the archaic notation is off-setting at times. Basically, if you're looking for straighforward information (written by a mathematician, for a mathematician), you've found the perfect book. If you're looking for an easy-to-read and understand book, keep searching.

Rating:
Summary: Calculus Volume 2 (Tom M. Apostol)
Review: tHERE IS A EXCELLENT BOOK.

Rating:
Summary: Calculus Volume 2 (Tom M. Apostol)
Review: This book contains a lot of information, and is rigorous, with many proofs and a vast array of problems. However, it is weak on worked examples and in explaining the concepts clearly. Diagrams are kept to a minimum. I used this book during an undergraduate Calculus course, and found that it did not help me to grasp the fundamentals of the subject. There are much better books available e.g. Stewart, which cover much of the same ground in a much simpler format. In my experience, only the ablest students were able to benefit from Apostol's dense writing style and scarcity of worked examples. Apostol does, however, include sections on matrix algebra and calculus which are not available in many other textbooks. There are also solutions to many of the problems at the end of the text.