What Is the Best Path to Tackle Goldstein's Classical Mechanics?

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Discussion Overview

The discussion revolves around the best approach to studying classical mechanics, specifically regarding the text "Goldstein's Classical Mechanics." Participants explore preparatory resources and the appropriate sequence for tackling these materials, considering the mathematical background required.

Discussion Character

  • Homework-related
  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant expresses a desire to skip directly to advanced topics in physics after completing precalculus and Apostol's calculus vol 1, seeking advice on how to approach Goldstein's text.
  • Another participant recommends starting with Kleppner, stating that the mathematical background from Apostol vol 1 is sufficient for it, and suggests following it with Taylor.
  • Concerns are raised about the differences in calculus presentation between Kleppner and Apostol, particularly regarding the use of infinitesimals in Kleppner.
  • The Feynman lectures are mentioned as a useful secondary resource, but not as the primary study material.
  • Questions arise about the timing of studying Goldstein in relation to Taylor, with uncertainty about whether Taylor covers the same material as Goldstein.
  • A later reply notes that Goldstein is generally considered a graduate-level text, indicating a significant jump in difficulty compared to undergraduate resources.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best order to study these texts, with differing opinions on the necessity of Taylor before Goldstein and the appropriateness of the recommended resources.

Contextual Notes

Participants express varying levels of familiarity with calculus and physics, which may influence their recommendations. The discussion reflects differing educational backgrounds and approaches to learning advanced physics.

Who May Find This Useful

Students preparing to study classical mechanics, particularly those considering advanced texts like Goldstein, and those seeking guidance on foundational resources in physics and mathematics.

Niceadam
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im 16,love physics, who is about to graduate school, before that i decided that school was too slow for me, so i decided to skip right to the good stuff...
did precalculus and 'How to Prove it' to start me on calculus.
i just finished Apostol's calculus vol 1 to prepare me for handling the mathematics to come in physics. i wanted to tackle Goldstein's classical mechanics but i heard its tough to handle without any background. i read that Taylor or Kleppner might be good to get me started as well as the Feynman lectures, what's your opinion?
my physics is at the level of freshman, but i can handle tough stuff..
and at what point do i need start learning multivariable, like say apostol vol 2?
 
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Niceadam said:
im 16,love physics, who is about to graduate school, before that i decided that school was too slow for me, so i decided to skip right to the good stuff...
did precalculus and 'How to Prove it' to start me on calculus.
i just finished Apostol's calculus vol 1 to prepare me for handling the mathematics to come in physics. i wanted to tackle Goldstein's classical mechanics but i heard its tough to handle without any background. i read that Taylor or Kleppner might be good to get me started as well as the Feynman lectures, what's your opinion?
my physics is at the level of freshman, but i can handle tough stuff..
and at what point do i need start learning multivariable, like say apostol vol 2?

I recommend doing Kleppner right now. If you know Apostol v1, then you definitely know enough math to do Kleppner. After Kleppner, you should do Taylor.
As for Apostol v2, this covers multivariable calculus. That is obviously important, so I wouldn't postpone it for long. But it's not necessary to know in order to do Kleppner.

A word of warning which might or might not bother you (it bothered me): the calculus as done in Kleppner is somewhat different from Apostol. Kleppner fully uses the language of infinitesimals, which never really appear in Apostol. This might be confusing. If you wish to see calculus as framed in the language of infinitesimals, see Keisler's free book: https://www.math.wisc.edu/~keisler/calc.html

The Feynman lectures are pretty great, but don't use them as main resource. They're useful as a secondary resource only. I recommend studying a chapter in Kleppner and then reading what Feynman has to see about it as a second opinion. You will probably want to revisit the same chapters in Feynman over and over again in your career...
 
Thanks, and how about Goldstein? should i do it after taylor? or does taylor cover as much goldstein?
 
Niceadam said:
how about Goldstein?
Goldstein is a graduate-school (post-bachelors) level text, except maybe at schools like MIT or Caltech.
 

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