Calculus, Volume 2

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. There is just enough theory to make the transition to analysis very smooth. These 2 books cover calc 1-2-3 and diff eq. plus some more. The author is very clear. Look for a cheaper copy on-line.

This volume is the hammer of the two volumes, where as the first volume would be the nail. Once you've master volume one it's time to start digging for gold; the basics one learns in volume one will be expanded to multi-variables and applications that will challenge even the most skilled students. The introduction of linear algebra is a good preview of the things to come for those interested in pursuing mathematics even further.

I used these books (Vols. 1 & 2) in my last two years of high school back in South America. I remember long nights of bad coffee and cigarettes locked in my room reading it over and over. The book is full of really cool knowledge (even for a non-mathematician). Most of today's students learn like little parrots, (without thinking or understanding) just repeating things mindlessly. This will make this book unpopular among these people because having to read a sentence and stop to figure things out on their own is too hard a challenge for them. I guess that like the high standard of the education of old when teachers loved teaching and their subject this book is also going the way of the dinosaurs. I'll get my copy before that if I were you though ;-)

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.

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.