Calculus Surprise The Gaussian Integral
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Awesome!
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Great stuff for those ppl who are doing this kind of math as a hobby =)
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Yeh who else hates the Gaussian integral?
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its a good video, however a little more explanation throughout would be even better, example: at the end of the video 6:50 you didn't mention that the if one were to do e^infinity - e^0 = 1. Although its generally assumed the viewer should know this, its sometimes still nice to mention it, since if you don't, the viewer would have to double check by pausing the video....
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9:34
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wow I thougth I can learn something watching this movie. but u just write down more and more stuff and getting from one line to the next is not explained at all. surprise! o_O
MistaSmith 4 months ago
@MistaSmith Good comment.... and Yes, this video assumes that the viewer already knows basic calculus and analytic geometry. So it's not for everybody.
Mathview 4 months ago
Rather than transforming the variables into polar ones, you can complete the volume integral simply by doing a solid of revolution about the y axis of the graph y=e^(-x^2). Putting in the limits [1,0], watching out for y*log[y] as y tends to zero, results in the volume being pi. So you square root for the single integral and there you go.
kind of nice because this method is contained within the A level syllabus.
spasman 8 months ago
@spasman Yes, good comment. [Alternate solution without polar coordinates] @spasman correctly observes: Construction of the volume, double integral, from elementary disks of square radius = log(1/y) reduces to a "do-able" single integral. Evaluation of the limits of integration is accomplished with an interesting limit of Lim [ y-> 0 ] of Log(y^y) = 0.
Mathview 8 months ago
I'm posting some revised versions of these older videos. You may want to view the revised version instead of the original.
Mathview 1 year ago
Good.
pollardrho06 3 years ago
Thanks,, I plan to do some more with a focus on special functions when I get back to this next month.
Mathview 3 years ago