Mathematical background concerning classical physics/mechanics.

[learnings_sweet]

Hello, I was wondering what mathematical skills I would need to have in order to grasp classical mechanics as a whole; Newtonian, Lagrangian and Hamiltonian.

I already have a small understanding of some classical concepts; such as motion in a two dimensional space (circular/arc motion, mechanics of a simple pendulum, projectiles, equilibrium, slopes etc.) and basic wave properties (phase, harmonics, superposition etc.). However, in pretty much all of these I was left with a concept and plugging numbers into what seemed as pretty abstract equations... I would really like to try and understand mathematical proofs behind these concepts, such as how to use calculus to derive centripetal acceleration to simply mention one.

If you would be able to cite good resources, mostly on line as cash is a bit of an issue, it would be much appreciated!

Side Note: If it helps I have an AS level year of maths and physics behind me, just so you can gauge the level of detail I'm capable of understanding.

 

[ShayanJ]

The math you need for understanding classical mechanics is not much. You should only have good understanding of calculus, differential equations and some vector analysis and also be able to follow/do some intense and long calculations which you gather only by practice. A knowledge of calculus of variations will also help you. And also matrices and determinants and just a little about tensors. You should be able to use different coordinate systems too.
If you want books that covers all of these(except calculus which you should know before learning other parts), I can suggest you Arfken's. Boas's book is good too but its on a little lower level than Arfken's.
Then you should read advanced books on classical mechanics e.g. Goldstein's, Marion's, Kibble's or any book in the same level.
But if you also mean classical electromagnetism, then things get a little different. Now you should be really good at vector analysis and again know a little about tensors. And a good book I can suggest is the one by Griffiths.

 

[jedishrfu]

Welcome to PF!

From my own experience, you calculus 1,2and3, differential equations and possibly linear algebra with that you should be well grounded to tackle it.

 

[learnings_sweet]

Thank you very much :)

 

[learnings_sweet]

The math you need for understanding classical mechanics is not much. You should only have good understanding of calculus, differential equations and some vector analysis and also be able to follow/do some intense and long calculations which you gather only by practice. A knowledge of calculus of variations will also help you. And also matrices and determinants and just a little about tensors. You should be able to use different coordinate systems too.
If you want books that covers all of these(except calculus which you should know before learning other parts), I can suggest you Arfken's. Boas's book is good too but its on a little lower level than Arfken's.
Then you should read advanced books on classical mechanics e.g. Goldstein's, Marion's, Kibble's or any book in the same level.
But if you also mean classical electromagnetism, then things get a little different. Now you should be really good at vector analysis and again know a little about tensors. And a good book I can suggest is the one by Griffiths.

Thanks again, any ideas on what I should know regarding classical thermodynamics as well?

 

[ShayanJ]

Heat and Thermodynamics by Zemansky and Dittman will teach you what you need!