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Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability 2nd Edition
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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.Read more ›
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.Read more ›
Most Recent Customer Reviews
The electronic version of this text book is terrible, and the app Yuzu that you are required to use is not at all practical for textbooks. Read morePublished 5 months ago by Amazon Customer
This review is about the printing quality of the hard cover book and not about the content itself. So, without no shame the contents section, the subsequent ones, and the first 12... Read morePublished 8 months ago by Amazon Customer
This book published in 1969 joined Vol.1, published in 1967, in my library. A fortunate purchase in 2010 (new, not used, and I think I wrote a first review), as I way back in the... Read morePublished 12 months ago by Rolf M. Mjelde
I like it. Explain things really in detail. I believe I can construst a srtong mathematical basis through reading this.Published on September 21, 2013 by Zhen Jiang
I ordered this book for my son for his Calc class at school. It arrived promptly and in perfect condition. He loves the book.Published on April 18, 2013 by A Ball
I have to say that this book is the worst textbook I have ever used in my math study.
Very messy notation. Why does the author use bold word to denote vector? Read more
The two volumes of Apostol's "Calculus" must be linked to his "Mathematical Analysis".
I consider "Mathematical Analysis" as the third volume, complement to Apostol's... Read more
if you have gone through the vol 1, then you do not need my review. I feel vol 1 and 2 are the best calc books for math majors. Read morePublished on June 29, 2009 by S. Shaikh