I cannot praise Courant's calculus lucid writing highly enough, and look forward to working though his Calculus texts in the future.

I think that calculus you calculus would find Apostol's book sufficiently rigorous, as spivak well as extremely intuitive.

For instance, Apostol introduces "little-o" notation, a cousin of "big-O" notation which is used extensively edition in computer science.

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I am a computer programmer currently, and am looking to go into mathematics exclusively.I also am a musician, and coupled with my computer programming experience it seems that perhaps we edition think alike.Org item description tags) archiveorg Calculus_643 width560 height384 frameborder0 webkitallowfullscreentrue mozallowfullscreentrue.I have the 1st edition and I think it's a great book, not dry at all.This is a book I would strongly recommend reading regardless of what calculus book you choose.Spivak's analogous book, "Calculus on Manifolds is known as an extremely difficult text, and is commonly michael used as an introduction to differential michael geometry (indeed, his comprehensive volumes on differential geometry mention Calculus on Manifolds as a prerequisite).Spivak's treatment is rigorous but also well-explained: he presents proofs for everything but also gives a good narrative explaining why the proofs are structured as they are, and why they work.That being said, Spivak has been described by some as a deep real-analysis text more than a calculus book, so you would still deeply cover all the fundamentals.The choice of book should also reflect your future interests.Whatever book you choose, recognize before you start it that you are running a marathon, not a sprint.It's also a very rigorous approach, and a very well respected book, however it starts more gently than Spivak's.

With Apostol I was able to understand and answer all the questions in the first few chapters much more easily, and then I saw the difficulty increase a bit; however it increases progressively throughout from the book.

Do as many of them as you can.

Apostol's annihilation is still, in my opinion, very well peppered throughout with applications; many chapters contain a specific "applications." section which links the theoretical concepts you just learned with the applied use of those concepts.

I agree wholeheartedly with mathwonk's statement that, although the books are difficult, reading different approaches and going over crack them multiple times is really what gives you a deeper understanding of calculus.

Many of the problems creating in the introduction of Apostol are exactly the same as those in Spivak, however the order and context that they are presented in leads you to the correct method for proving them, whereas Spivak's are more isolated.I would say that Apostol's book might serve you a little better in this total respect as well, as it is slightly tilted towards analysis, whereas Spivak's is tilted towards differential geometry.The exercises are fantastic!The Should I Become a Mathematician?As an added bonus, Apostol's Calculus covers linear algebra as well, and the second volume covers multivariable calculus.Mathwonk also mentions that most students find Apostol very dry and scholarly, where Spivak is more fun; however, I have not found this to be the case.I have worked through every problem in Apostol's Calculus through chapter 10 so far, and it has been a joy spivak (most times).Another set of calculus books which I own and are held in high regard are Courant's.Org item description tags) archiveorg lculus3rdEd.1994 width560 height384 frameborder0 webkitallowfullscreentrue mozallowfullscreentrue.With Spivak's book, the problems start out extremely hard, and get easier servicedesk as the book goes on (mostly by getting used to his annihilation style, not objectively).My brief skim of them, as well as other's comments, suggest that they are more focused on applications perhaps than some of the other books.My only exposure to Courant's expository style comes from his excellent book.

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