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Is there a very good book covering the whole calculus in detail, explaining all topics in calculus 1-3 for self-learning? I'm in geometry I, so I will start calculus in two years, and finish in five years. But I don't care, I'm way ahead of everyone in my school and I already know calculus 1 and half of calculus 2. I just need to cover it again in very good detail because all that I know about it is unstable as there are no very good books that I can find nor very good tutorials online.

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  • $\begingroup$ If you've seen calculus 1, why not just try out elementary analysis? Ken Ross's book is very friendly, and if you've seen induction, is probably accessible to you. If you're looking specifically for a calculus text, I like Zorich's book. The two volumes cover everything you're looking for, and are rigorous. $\endgroup$ – Alfred Yerger Apr 30 '16 at 3:31
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    $\begingroup$ Calculus by Tom Apostol (two volumes) is entirely comprehensive and rigorous. $\endgroup$ – MathematicsStudent1122 Apr 30 '16 at 3:31
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    $\begingroup$ @KKZiomek Zorich's book goes through a solid amount of theory and applications. It is aimed at the serious student of mathematics that is capable, but has never seen calculus before. It can be a little terse at times, as he often writes things formally. It covers everything you would find in a "basic analysis" course, but also applications in computation and the sciences. Over the two volumes, it includes multivariable calculus, and a plethora of other interesting and advanced topics. $\endgroup$ – Alfred Yerger Apr 30 '16 at 3:47
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    $\begingroup$ If Zorich's text seems too advanced, or rather, if you're looking to be introduced to calculus int the way taught by many US high schools and colleges, try Thomas' Calculus. It's an undergraduate level texts with solid exposition. Easily digestible. It will set you up with the major theorems and machinery of calculus, including vector based applications. It's not a substitute for a book on analysis. The fact that you mention Calc 1-3 makes me think this book may suit you better than other options. $\endgroup$ – zahbaz Apr 30 '16 at 3:57
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    $\begingroup$ A very standard textbook is Stewart's Calculus. I don't necessarily recommend it, but you should at least be aware of it. $\endgroup$ – littleO Apr 30 '16 at 8:35

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