Resources on the Derivation of generalized Stokes' theorem

  • #1
PhysicsRock
116
18
Hello everyone,
as part of my bachelor studies, I need to attend a seminar with the aim to prepare a presentation of about an hour on a certain topic. I have chosen the presentation about the generalized Stokes theorem, i.e.

$$
\int_M d\omega = \int_{\partial M} \omega.
$$

After hours of searching, I unfortunately haven't found any resources on the internet. It seems like all there is is proofs, not derivations. My professor has given us some literature recommendations, however, they're not available in our library and certainly not free, costing about 150€ each.
Perhaps one of you has encountered a similar issue and can tell me where to look. Of course, both the internet and literature are fine, maybe one of your recommendations is available in the library or on the second hand market, which is a lot cheaper typically.
Just to be avoid pointless efforts, here's the list from my professor:
Altland, von Delft: "Mathematics for Physicists: Introductory Concepts and Methods"
Thirring: "A Course in Mathematical Physics 2"
Lechner: "Classical Electrodynamics: A Modern Perspective"
 
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  • #2
Exactly what do you consider to be the difference between a proof and a derivation?
 
  • #3
Orodruin said:
Exactly what do you consider to be the difference between a proof and a derivation?
To me, a proof means starting with the theorem and ending somewhere else, a true statement would be good.

A derivation would do the same, but the other way around. Start somewhere, do some math-magic and finish off with the theorem.
 
  • #4
PhysicsRock said:
To me, a proof means starting with the theorem and ending somewhere else, a true statement would be good.

A derivation would do the same, but the other way around. Start somewhere, do some math-magic and finish off with the theorem.
Then you need to revise what you think a proof is. A proof is a logical argument for why a statement must be true. Showing that A implies B, where B is true, does not make A true.
 
  • #5
Orodruin said:
A proof is a logical argument for why a statement must be true. Showing that A implies B, where B is true, does not make A true.
True, my mistake. I guess I'll ask my professor if a proof would do the job, assuming we already know the theorem and just wanted to confirm it's true, not build it from scratch / a certain point we can assume to be true.
 
  • #6
PhysicsRock said:
Hello everyone,
as part of my bachelor studies, I need to attend a seminar with the aim to prepare a presentation of about an hour on a certain topic. I have chosen the presentation about the generalized Stokes theorem, i.e.

$$
\int_M d\omega = \int_{\partial M} \omega.
$$

After hours of searching, I unfortunately haven't found any resources on the internet. It seems like all there is is proofs, not derivations. My professor has given us some literature recommendations, however, they're not available in our library and certainly not free, costing about 150€ each.
Perhaps one of you has encountered a similar issue and can tell me where to look. Of course, both the internet and literature are fine, maybe one of your recommendations is available in the library or on the second hand market, which is a lot cheaper typically.
Just to be avoid pointless efforts, here's the list from my professor:
Altland, von Delft: "Mathematics for Physicists: Introductory Concepts and Methods"
Thirring: "A Course in Mathematical Physics 2"
Lechner: "Classical Electrodynamics: A Modern Perspective"
Not sure what you are looking for but Lee's Introduction to smooth manifolds chapter in Integration of forms is a great source. I believe the first edition is freely available as a pdf.
 
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  • #7
jbergman said:
Not sure what you are looking for but Lee's Introduction to smooth manifolds chapter in Integration of forms is a great source. I believe the first edition is freely available as a pdf.
Thank you. I'll check that out.
 
  • #8
I suspect DoCarmo's book on differential forms may have something on it too.
 
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  • #9
WWGD said:
I suspect DoCarmo's book on differential forms may have something on it too.
Great, thank you!
 
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  • #12
romsofia said:
https://sites.science.oregonstate.edu/physics/coursewikis/GDF/book/gdf/stokes.html is a non "proof" version, but if you're giving an hour-long talk, probably going to need to throw some proofs in there for filler.
This is actually brilliant, because Stokes by itself works without a metric, but I'm still supposed to cover how one may appear when considering the Hodge-Star, which is included here. Amazing, thank you!
 
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