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# Multivariable Calculus watch

1. I was looking for a proof of E=mc^2, when I found this website.

http://library.thinkquest.org/3471/e...uivalence.html

All of it seems rather simple bar a little bit.

it is right below the line "the expression for kinetic energy becomes"

Why does the limit change from mv to v when m is expressed in terms of constants and v? Also why does the limit change from s to mv when the integral is changed from ds to dmv?
2. As S changes from 0 to the final value of s, Mv changes from 0 to the final value of Mv.

So I guess that is why the limit can be changed from s to mv, as the value of mv is reached at distance s.

Just a guess....
3. Hmm, no change of limits in my notes for special relativity. However, it's probably because you're switching around the differentials like steven said. Anyway, in our lecture mathematicians were told to close their eyes while the lecturer did these manipualtions, hinting that it's a rather non-rigorous process.
4. If you sub s=mv into the original integral and remember that v=ds/dt the result follows. I think Steven's explanation for the physical argument is reasonable.
5. (Original post by nota bene)
If you sub s=mv into the original integral and remember that v=ds/dt the result follows. I think Steven's explanation for the physical argument is reasonable.
Any take on the m disappearing?

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