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Mar
26
asked Reference Request: Classical Mechanics with Symplectic Reduction
Jan
12
comment Electromagnetism for Mathematician
@Christopher White please read my above comment
Jan
12
comment Electromagnetism for Mathematician
In addition, I have seen in Special Relativity have a 2-form called action and saw that electric field and magnetic field can be read from by looking at specific coefficients of its components. However, I do not understand how and why you can read these fields from that in that specific coordinates. To specify, I meant from here: math.toronto.edu/~drorbn/classes/0708/GeomAndTop/Maxwell.pdf
Jan
12
comment Electromagnetism for Mathematician
I have taken look at that book and it does not seem to prove Maxwell's equation from Biot-Savart's law and etc (as how Maxwell would approach from historical point of view?)
Nov
24
comment Electromagnetism for Mathematician
Actually best thing is EM in more general setting if that is possible (maybe what happens to Maxwell's equation if our ambient space is any smooth manifold, instead of usual Euclidean space?). EM on low-dimensional manifolds would be cool, but if it does right on Standard Euclidean space, that is fine with me.
Nov
24
comment Electromagnetism for Mathematician
Thank you for good comments. It is just I was looking up Maxwell's equation in Griffth&Harris and later in wikipedia I figured out that dirac delta is indeed a distribution (this fact was nontrivial, as my interest is more onto differential topology and abstract algebra (not sure on analysis)). Before I move further, I was just hoping for good EM book done right, maybe giving full rigorous proof of important results that I might possibly get stuck in future.
Nov
24
awarded  Editor
Nov
24
revised Electromagnetism for Mathematician
edited body
Nov
24
asked Electromagnetism for Mathematician
Sep
30
comment reference request: Classical Mechanics as an Application to Smooth Manifolds
Just in case you are curious about other discussion (maybe my question is possibly a duplicate compared to these links, but the spirit of the question asked is more specific here) physics.stackexchange.com/questions/23107/… , physics.stackexchange.com/questions/9165/…
Sep
29
asked reference request: Classical Mechanics as an Application to Smooth Manifolds
Apr
1
comment Classical Mechanics for Mathematician
On the related question, people seem to mention Goldstein, but he does not relate mechanics to manifolds.... Do you think Goldstein is just for physicists? Or is it a good intermediate book before Abraham/Marsden?
Apr
1
awarded  Student
Apr
1
asked Classical Mechanics for Mathematician