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I'm curious as to whether or not Spivak's Calculus is the way to go as an introduction to calculus. I'm reading Velleman's How To Prove It? at the moment to get a better grip on proof writing. I have had minimal exposure to calculus (I put emphasis on minimal), so I'm wondering if this will hinder my learning experience.

Thanks!

Arthur
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DamonLikesPhysics
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  • Notice that this response is a comment, not an answer. Personally, I would (blindly) suggest either Spivak or Apostol - "Calculus 2nd Ed." (1966 : two volume work). The choice would be determined by how important you feel that it is to be able to "prove" as you go, as Apostol does. Actually, I don't know anything about Spivak's version other than that it (also) has a very good reputation. For all I know, Spivak may also "prove as he goes". If you are not totally comfortable with the "prove as you go" approach, then I would not recommend Apostol. – user2661923 Sep 27 '20 at 08:34

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If you like How To Prove It, you might check out: Velleman, Calculus: A Rigorous First Course.

Dan Velleman
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    Especially in a thread like this, I think you should say a little more about why you're recommending this book. – Integrand Sep 29 '20 at 01:39
  • It is, like Spivak, a rigorous calculus book that doesn't require any prior knowledge of calculus. I mentioned it because the OP said he is reading How To Prove It. This book is by the same author (namely, me), so if the OP likes How To Prove It he might like this book as well. If you want more about how my book compares to Spivak: Spivak focuses on the theory behind Calculus, and it is rigorous. A book like Stewart focuses on how to solve Calculus problems, and it is not rigorous. My book is in between: it focuses on solving problems but it is rigorous. – Dan Velleman Sep 29 '20 at 17:15