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Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability 2nd Edition

3.8 out of 5 stars 23 customer reviews
ISBN-13: 978-0471000075
ISBN-10: 0471000078
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Editorial Reviews

From the Publisher

Now available in paperback! An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.
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Product Details

  • Hardcover: 673 pages
  • Publisher: Wiley; 2nd edition (June 20, 1969)
  • Language: English
  • ISBN-10: 0471000078
  • ISBN-13: 978-0471000075
  • Product Dimensions: 7 x 1.2 x 10.3 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (23 customer reviews)
  • Amazon Best Sellers Rank: #292,873 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

Format: Hardcover
Apostol's Calculus is the definitive book on Calculus for anyone who wants to be a mathematician. Historical notes, intuitive ideas, clear definitions, demonstrations, all is there, from natural numbers to Stokes' Theorem. His applications of linear algebra to multivariate calculus are among the best I have seen on calculus textbooks Better than this, only a book on Mathematical Analysis.
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Format: Hardcover
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.
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By Raman on August 24, 2004
Format: Hardcover
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.
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Format: Hardcover
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.
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Format: Hardcover
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.
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Format: Hardcover
The author is a world renowned mathematician, with many beautiful achievements under his belt. I would not include this popular textbook in this category.

I tried to use it for my real analysis class but I decided otherwise when I opened the first volume. I believe strongly that the key concept underlying real analysis is the concept of convergence/continuity. What turned me off from this book was his consistent effort to avoid this concept for the first half of the first volume which deals with rather sophisticated convergence problems involving Riemann/Darboux sums.

The choice of opening a beginner's book on analysis with Riemann integral is rather unusual. In itself, being unusual is not a negative, but in this special case I do not believe it is helpful. I believe that in learning one should start with simpler examples and gradually increase the difficulty. In this book the reader is thrown in some of the most complex situations, while deliberately avoiding the two ton gorilla in the room. This is not how this reviewer and many of his students learn a new theory.

What is then a young reader to do? I have two strong recommendations. The first is the classic text by G.H. Hardy, A course in pure mathematics. This old classic is still relevant today. Hardy was an elegant writer with a beautiful mind, arguably one the best analysts of the 20th century. His book has rigor, geometric intuition, beautiful examples, and a genuine empathy for the green mind. Some exercises in this book can be a bit challenging, but always very rewarding.

The second recommendation is Terry Tao's textbook on real analysis. His is arguably one the the best analysts alive, and he has a keen sense of the traps awaiting the modern students.
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