Book preparing me for Goldstein

[Niceadam]

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?

 

[micromass]

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...

 

[Niceadam]

Thanks, and how about Goldstein? should i do it after taylor? or does taylor cover as much goldstein?

 

[jtbell]

how about Goldstein?

Goldstein is a graduate-school (post-bachelors) level text, except maybe at schools like MIT or Caltech.