Recommendations for a calculus refresher

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SUMMARY

The discussion centers on recommendations for self-studying calculus to reach a Calculus III level, essential for progressing to differential equations and vector calculus. Participants suggest using the Kline Calculus book for its reputation, while also recommending "Calculus and Analytic Geometry" by George Thomas and "Calculus" by Tom Apostol for their comprehensive coverage. The emphasis is on the importance of solved examples and a focused approach to understanding differentiation and integration techniques.

PREREQUISITES
  • Basic understanding of calculus concepts, including differentiation and integration.
  • Familiarity with mathematical problem-solving techniques.
  • Access to calculus textbooks, specifically Kline Calculus, Thomas' Calculus and Analytic Geometry, and Apostol's Calculus.
  • Commitment to self-study and practice through solved examples.
NEXT STEPS
  • Explore the Kline Calculus book for foundational calculus techniques.
  • Study "Calculus and Analytic Geometry" by George Thomas for a comprehensive review.
  • Review "Calculus" by Tom Apostol for deeper theoretical insights.
  • Practice solving calculus problems to reinforce understanding of differentiation and integration.
USEFUL FOR

Students returning to calculus, self-learners preparing for advanced mathematics, and anyone aiming to strengthen their calculus skills for applications in physics and engineering.

ibkev
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Hi all - I took engineering a while back and haven't used calculus in a very long time. I'm looking to get back up to speed via self study to a calculus III level so as a next step I can move into differential equations and vector calculus. (My real goal is to work through a self study of undergrad physics.)

I more/less remember how to apply calculus but have long forgotten the mechanics of the various differentiation/integration techniques, etc. I picked up the Kline Calculus book because it is both cheap and highly regarded. Having spent some time with it, I can see why it's highly regarded but, because it contains lengthy applications interwoven with the calculus techniques, I'd like something more succinct and math focussed.

Can anyone recommend such a text? Since I'm doing self study, lots of solved examples are valuable to me.
 
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Hi Ibkev,

I am in a similar situation than you: I started to study by myself quantum physics some time ago, and, in the process, I realized I had to to take my old calculus books.

In my case these books are two: an old edition of Calculus and Analytic Geometry by George Thomas as well as Calculus by Tom Apostol. You better be ready to struggle at the time to review these sort of topics and books, and, I confess, in the beginning you can feel overwhelming, but, later you will enjoy them: the main motivation you can use is to come back to be familiarized with these topics, and then, everything will become easier. As for my recent experience you need to read solved examples, and, to study theory as well.

You are in the right place: many people here are willing to help other as us.

Good luck
 
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