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 DieCommie
Registered: 12/11/03
Posts: 29,258
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 Re: What classes are you taking in the Fall?  [Re: Chespirito]
#10208764 - 04/21/09 05:33 PM (14 years, 11 months ago) |
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What kind of stuff do you apply it to in science? I have heard of it, but dont know what it is.
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Chespirito
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Registered: 02/13/09
Posts: 3,259
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Re: What classes are you taking in the Fall? [Re: DieCommie]
#10208926 - 04/21/09 05:53 PM (14 years, 11 months ago) |
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Well we used it during part of the class to go over calculus of variations. For instance as Im sure you are more than aware of, the first variation is what gives us the Euler-Lagrange equations. There is uses for the second variation, think of it as the second derivative similar to the second derivative test to determine a min or max. The Euler-Lagrange equations just assures us that delta S is equal to 0, we are not interested in whether we are at a saddle, min or max. Anyways to determine the second variation is much more complicated and involves some special cases. For instance convex functions are relatively easy to find the second variation. Lie Brackets and Lie derivatives help in determining the geometry of the function we are dealing with which has a lot of uses in this subject including and besides the second variation. While Ive never taken one, you might be able to find a class on Classical Mechanics that's a second or third year grad course. They cover mathematical aspects of Classical Mechanics that you would never see in the normal courses. I doubt theres too much practical use unless you want to delve pretty deeply into theoretical physics though.
As for other uses, well you will probably see it in your Quantum Class presumably. You will probably use Sakurai's book and I believe it covers, (Unless im confusing it with that cat whose names starts with a B), the Special Unitary groups. These and other aspects of group theory seem pretty abstract at first but actually end up being really useful in quantum. For instance you can cut out a lot of work by understanding which operators will commute with each other, and figure out symmetries which will tell you the level of degeneracy and where it comes from. blah and so forth, Cool stuff.
Im not sure what field of physics you want to go into but if its Field Theory Id recommend taking as much math as you can. Shit I was an EE major, I basically had no use for a lot of what I took but it was cool stuff. Actually some of it did apply to solid state physics so I guess it had some use.
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Chespirito
Stranger
Registered: 02/13/09
Posts: 3,259
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Re: What classes are you taking in the Fall? [Re: Chespirito]
#10208943 - 04/21/09 05:56 PM (14 years, 11 months ago) |
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I just found this link:
http://www.physics.drexel.edu/~bob/LieGroups.html
Apparently a free text on Lie Groups. The subject is gigantic and I don't pretend to know more than a very small fraction of it.
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DieCommie
Registered: 12/11/03
Posts: 29,258
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Re: What classes are you taking in the Fall? [Re: Chespirito]
#10209112 - 04/21/09 06:17 PM (14 years, 11 months ago) |
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Cool. Yea, I think for the work Im going to be doing Ill have to learn in some part QFT and QED. Sounds good to me. 
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 canid
irregular meat sprocket
Registered: 02/26/02
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Loc: looking for zeebras, n. c...
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Re: What classes are you taking in the Fall? [Re: c0sm0nautt]
#10209536 - 04/21/09 07:13 PM (14 years, 11 months ago) |
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home vegetable production: 0 credits,
soil sciences in agriculture: 0 cridits,
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earth building with adobe and cob: 0 credits,
PHP with MySQL: 0 credits,
LAMP server administration: 0 credits,
Javascript: 0 credits,
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another semester of self education: costless...
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If you detect a scent reminiscent of Anethole (anise) please preserve a specimen or two for study and please PM me.
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