I'm going to study calculus and want to know which of these 2 books options, Spivak's Calculus and Calculus on Manifolds or Courant's Differential and Integral Calculus 1 & 2, is better to learn Calculus in a Theoretical way. Can you tell me which is best for my purpose?
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FYI, for Courant's Introduction to Calculus and Analysis (Vol. 1) I gave my views here (see also here and here), and there is a solution manual for Courant's Introduction to Calculus and Analysis -- Albert Abraham Blank, Problems in Calculus and Analysis, John Wiley and Sons, 1966, x + 264 pages. archive.org copy. – Dave L. Renfro Feb 07 '20 at 07:10
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My suggestion, based mostly on personal preference, would be to go first through Spivak's Calculus. The exposition is very good, and the exercises are lovely. That said, I would compare with Courant along the way.
Calculus in Manifolds is a different beast. It is nice, and definitely enjoyed it, but it is brutal, and it is not the way to get started with several variable calculus in my opinion. So, for several variables I would first look into volume II of Courant, and only then read Calculus in Manifolds.
Martin Argerami
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I started working through Courant's recently. It is dense but has lots of interesting little points along the way. I don't have much to say about Spivak's but I've heard that if you have had any amount of exposure to Calculus before, it is better to go through Courant. I've also heard that while Spivak's Calculus is incredible, Calculus on Manifolds isn't the best the use. One last consideration is to consider the purpose of your studies. Courant offers lots of applications and is meant for the engineer or scientist who wants to learn Calculus right.
As an aside, there is a very good theoretical book that many people suggest by Apostol. I'd look into that as well.
Edd
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