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I want to master calculus in every possible way, I'm working in my bases like algebra and trigonometry (Precalculus) since I haven't had a good start in calculus, I want to read books like Calculus by Spivak, Calculus by Apostol and Courant books from Calculus and analysis.

I want to know which books of calculus those 3 authors (Stewart, Larsom, Thomas) could help me to make a good aproach to calculus, if they are any substantial differences, if you think they are others best books please tell me

joseph morrison
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    Context is everything in this question. If you're more of a "visual", or example-based learner, look for titles with the words "for Engineers" in them. Study small but real problems - gravity, motion on a cycloid, etc. (Gilbert Strang's Calculus does a good job) When you get tired of mathematicians calling you lazy, and wondering how your right answers are still somehow wrong, move into texts that treat the subject more formally: Spivak, DoCarmo and the like. –  Jan 20 '21 at 18:26
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    For a smoother ushering into calculus, you might want to look into the Demidovich problem book--calculus doesn't begin until problem 136, so the first 135 are a good test of readiness. – avs Jan 21 '21 at 01:18
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    I don't think which of Stewart, Larson, Thomas you study from will matter, as all three cover essentially the same topics at the same level and have benefited from many years of wide usage. More important is to learn how to read and learn from a math text, working a lot of the exercises, and pursuing in other books or online a few topics you might be interested in (which might be something mentioned in the text or an exercise that sparked your interest). I recommend waiting until later to further plan your future, and for now just concentrate on fully mastering one of these three books. – Dave L. Renfro Jan 21 '21 at 12:59

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Among the modern literature, I haven't seen anything more comprehensive, application-connected, and thorough than Zorich's 2 volume.

Maybe even precede a study of Zorich by studying the first 3 chapters of Kolmogorov & Fomin, which is likely to save you a lot of time.

avs
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  • Are those book readable for a first approach to Calculus? – joseph morrison Jan 20 '21 at 19:05
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    Yes, absolutely. Zorich and Kolmogorov take it from the ground up. They come from an academic tradition where the instructors deeply cared about the students' ability to progress. – avs Jan 20 '21 at 20:18
  • Thank you very much,, I'm going to check it. – joseph morrison Jan 20 '21 at 20:44
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    When someone says they're working on algebra, trigonometry, and precalculus and mentions possibly wanting to then study from Stewart's or Larson's or Thomas' calculus texts, a book that includes differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions is utterly inappropriate, made even worse by saying maybe precede by studying from a graduate level real measure theory and functional analysis text. I would guess that less than 1% of those at the OP's level will ever reach this level. – Dave L. Renfro Jan 20 '21 at 23:55
  • @DaveL.Renfro Come on. Differential forms on manifolds are not reached in Zorich until page 300, and even then only as an expression--without the context of a manifold (postponed till Vol. II).

    As for Kolmogorov and Fomin being "graduate level", this classification is used in the US colleges that have had to water down their mathematics program, but in all decent curricula around the world topological spaces are introduced in the same year, if not in the same term, as metric spaces, as they should be. A Bachelor's in mathematics who doesn't know topological spaces, has been ripped off.

     – avs Jan 21 '21 at 01:06
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    The OP is roughly asking which of Stewart, Larson, Thomas to begin, in order to later be able to read books like Spivak, Apostol, Courant. This puts the OP at a U.S. last year HS level or a U.S. just beginning college level. In particular, the OP has probably not had any exposure to non-calculational (i.e. proof-based) mathematics except maybe HS geometry. – Dave L. Renfro Jan 21 '21 at 08:21
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    Kolmogorov & Fomin is an excellent well-paced and comprehensive introduction for that, and chapters 1-3 do not even require a first acquaintance with calculus. It is not "graduate level". Someone who graduates with a Bachelor's in mathematics without knowing those 3 chapters cold, has been cheated out of an education.

    Anyway, there is no great risk to the OP to try those books. In the worst case, s/he will find them unsuitable rather early in the game, so no great loss of time will have occurred.

     – avs Jan 21 '21 at 18:47
  • BTW, the perpetuation of the learned mathematical helplessness in U.S. education is a lot more harmful than exposure to good materials. A student who doesn't know that they "can't do that kind of math because they've never seen it before" can do surprising well. Anticipation of a mental barrier often helps creates the barrier, becoming a self-fulfilling prophecy. Let's see how the student does actually. – avs Jan 21 '21 at 18:52
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    Zorich demands much greater mathematical maturity, and goes into far greater depth than the likes of Stewart, Larson, and Thomas. They are really not comparable. And someone wanting to choose between Stewart, Larson, and Thomas will likely not want to read Zorich (yet). OP states that they want to read Apostol, Spivak, and Courant. If they can read Zorich at this points, they should just skip right into Apostol, Spivak, and Courant. – Richard Sullivan Jun 09 '21 at 16:31
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My teacher recommended this. It's great, trust me!

https://www.springer.com/gp/book/9783319127712

Malandrino
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