Calculus, An Intuitive and Physical Approach

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1. rramadassAug 2026
   Some good books for introductory Calculus;

   1) Calculus: Basic Concepts for High Schools by Lev Tarasov. Soviet-era book written as a dialogue between the author and reader. Absolutely fantastic (also see his other books on Probability etc.) - https://mirtitles.org/2018/09/04/calculus-basic-concepts-for...

   2) Calculus: An Intuitive and Physical Approach by Morris Kline. A classic; any book by Morris Kline is a must-have - https://store.doverpublications.com/products/9780486404530

   3) Calculus: The Princess of Mathematics by H.C.Verma et al. A two-vol must-have affordable set. The author is a well-known Indian Physics professor and this is written specifically for students to "understand" calculus i.e. it is not a typical textbook. - https://garudalife.in/calculus-the-princess-of-mathematics-v...

   4) How to Think about Analysis by Lara Alcock. Provides conceptual insight like the Tarasov book above. Checkout the author's other books too. - https://global.oup.com/academic/product/how-to-think-about-a...

   I believe we need to study Calculus alongside Probability/Statistics nowadays due to their pervasive use in ML/AI/etc. To that end;

   a) Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming. It is by Hamming so one of the best. - https://store.doverpublications.com/products/9780486439457?_...

   b) Calculus and Statistics by Michael Gemignani. Similar to the above - https://store.doverpublications.com/products/9780486449937

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2. domnomnomNov 2022
   Calculus - an intuitive and physical approach. I did some of these exercises and they were easy. They helped me in calculus. I liked the explanation of secant lines.

   How to prove it - I like the reduction of proofs to mechanical symbol pushing. Good exercise difficulty for self study, good notation.

   I also liked some parts of the traditional calculus book. I read a lot of it. It’s pretty good considering literally everyone takes the class with the book. I would never use this for self study, but I enjoyed it during class.

   Mathematics for physicists books provide a good overview of math topics. Haven’t really done any exercises though.

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3. rramadassOct 2019
   In addition to all the other good suggestions, the following are recommended (have not seen these mentioned so far);

   - Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...

   - Methods of Mathematics Applied to Calculus, Probability, and Statistics - https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... (all books by Richard Hamming are recommended)

   - Calculus: An Intuitive and Physical Approach - https://www.amazon.com/Calculus-Intuitive-Physical-Approach-...

   For a Textbook reference, the following are quite good;

   - Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences - https://www.amazon.com/Mathematical-Techniques-Introduction-... (easy to read and succinct)

   - Mathematics for Physicists: Introductory Concepts and Methods - https://www.amazon.com/Mathematics-Physicists-Introductory-C...

   For General reading (all these authors other books are also worth checking out);

   - Mathematics, Queen and Servant of Science - https://www.amazon.com/Mathematics-Queen-Servant-Science-Tem...

   - Mathematics and the Physical World - https://www.amazon.com/Mathematics-Physical-World-Dover-Book...

   - Mathematician's Delight - https://www.amazon.com/Mathematicians-Delight-Dover-Books-Ma...

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4. lohengrammMay 2018
   I learned Calculus myself through a book called "Calculus - an intuitive and physical approach", by Morris Kline. It is cheap and very didatic.

   I never really studied physics, but I found the first books from the "Feynman lectures on Physics" to be very good.

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5. billswiftMar 2012
   It depends on what you want; I came at calculus mostly from a civil and mechanical engineering point of view, and I found the Dover reprint of Morris Kline's Calculus: An Intuitive and Physical Approach, originally published in 1968, very helpful.
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6. billswiftNov 2009
   I studied calculus on my own in my twenties, and I think the textbooks' focus on rigor led me down a lot of blind alleys before I started trying to come to an intuitive, often graphical, understanding of the problem before attacking the rigorous view. (There is a good textbook from 1977 that was reprinted by Dover in 1998, Morris Kline's "Calculus: An Intuitive and Physical Approach", that I wish I had available when I was studying.)
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