Any recommendations for a calculus and physics book for a beginner?

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Discussion Overview

The discussion revolves around recommendations for calculus and physics books suitable for beginners, particularly those who have completed the AP Calculus BC and AP Physics B curricula. Participants explore various texts that could help bridge the gap between basic understanding and more advanced concepts, including analysis, proofs, and specific areas of physics like particle physics and quantum mechanics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses a desire to deepen their understanding of calculus concepts, particularly through proofs, and seeks recommendations for books.
  • Another participant suggests that learning linear algebra, multivariable calculus, and differential equations may be more beneficial before tackling analysis, but acknowledges that pursuing analysis could be a fun challenge.
  • Some participants recommend "Analysis, with an Introduction to Proof" by Lay for its clarity and helpfulness in teaching logic and proof methods.
  • There is a discussion about the merits of "Spivak's Calculus," with some participants praising its presentation while others caution that it may be too challenging without prior proof experience.
  • Concerns are raised regarding the lack of a solution manual for Spivak's book, leading to uncertainty about self-study effectiveness.
  • One participant mentions that "Ross" is a good textbook for self-study, highlighting its examples and exercises, while noting that it begins with topics like infinite sequences and series.
  • Several participants share their experiences with Spivak's book, noting its informal presentation style and the challenges it poses, as well as the existence of errors in the text that may complicate self-study.

Areas of Agreement / Disagreement

Participants express a mix of opinions on the suitability of various books, with some favoring Spivak for its depth and others warning against it for those lacking proof experience. There is no consensus on which book is definitively better, as preferences vary based on individual backgrounds and learning goals.

Contextual Notes

Some participants highlight the limitations of their prior calculus education, suggesting that it focused more on computations than on theoretical understanding. This context may affect their readiness for more advanced texts.

Who May Find This Useful

Readers interested in transitioning from basic calculus to more advanced topics in analysis and proofs, as well as those looking for recommendations on physics texts related to particle physics and quantum mechanics.

  • #31
EighthGrader said:
Did you go through Spivak and Velleman at the same time? How much did Velleman help?

And when you went through Spivak, did you answer all of the problems at the end of each chapter?

I went through (part of) Spivak, and then started Velleman. I wish I'd gone through Velleman first. Velleman is much "gentler" than Spivak in introducing one to proofs. Although Spivak is apparently the most "gentle" of the theoretical calculus books, I still found him at times terse and difficult to understand. Lay may be a better alternative if you don't want two books, but I am really liking Velleman. Also, Spivak seems to be a favored text for many people and classes, so that's worth keeping in mind.

I did not do all of the problems in the sections of Spivak that I worked through. I looked at all of them and did maybe 1/3 to 1/2 of them.
 

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