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Before entering the university I studied the book "University Physics with Modern Physics" (written by Young and Freedman). In that time I used to study physical problems with methods taught by that book.

Now I'm math student at a university and I'd like to study a mathematical model of Classical Physics and solve some physical problems using this model. For example: I would like a model in which I can formalize and prove that the electrical potential energy inside a hollow charged spherical condutor is constant and I also want to formalize and find, in this model, the electrical field along the x-axis from a uniformly charged disk.

I'm only interested in models of Classical Mechanics (maybe using Symplectic or Poisson Geometry) and Maxwell's electromagnetism.

My question is: which book or article teaches a good mathematical model of Classical Physics? Please give some references.

The following PDF show more or less what I'm looking for: Notes on Mathematical Physics for Mathematicians (written by Daniel V. Tausk).

If you know one model, please, show how to formalize in this model one of the two examples I wrote before.

Thank you for your attention!

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    $\begingroup$ To what extent does your own reference (to Tausk) not answer your goal? $\endgroup$
    – LSpice
    Commented Apr 9, 2022 at 19:41
  • $\begingroup$ @LSpice I liked that PDF, however I want more than one reference. $\endgroup$
    – rfloc
    Commented Apr 9, 2022 at 21:15
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    $\begingroup$ I wonder if professional physicists really refer to that book as being due to Freedman and Young. I may be showing my age, but I would have called it “Sears and Zemansky” since they are the original authors: look at the cover more carefully. Freedman and Young came on board since S & Z eventually died (1975 and 1981). I don’t know the publication history of their book that well, but it feels analogous to (not identical to, just analogous to) calling the Feynman Lectures “Leighton and Sands”. $\endgroup$
    – KConrad
    Commented Apr 9, 2022 at 21:28

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For a mathematically rigorous treatment of electrodynamics, see The Mathematical Theory of Maxwell’s Equations by Kirsch and Hettlich.

For classical mechanics the "classic" reference is V.I. Arnold's book.

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