Complexifying the Integral (Arthur Mattuck, MIT)

Prof. Arthur Mattuck, of the Dept. of Mathematics at MIT, describes the usefulness of a technique for taking an integration problem into the complex plane by exploiting Euler's Formula.

This clip was taken from the Prof. Mattuck's class "18.03 Differential Equations" and can be found at:
http://ocw.mit.edu/18-03S06

The complete version of this specific lecture can be viewed at:
http://www.youtube.com/watch?v=EQJBp6Ym-6A

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[Ghaiyst]

This isn't easier than integrating by parts, but it's much more efficient. It doesn't take much to learn integration by parts, but this takes a little more to learn. Most specifically, what strikes my confusion (although I can apply it) is the reason why he says e^xi=cosx+ isinxwhen e^xi is cosxand therefor isinx could practically be anything as long as its imaginary. Why would he choose isinx? does it have something to do with a precal thing that I missed?

[hamsterpoop]

@Ghaiyst

Wikipedia: Euler's formula

[jimztar]

This is an awesome video, but you did forget the ' + c '

[pollardrho06]

My favorite professor at MIT.

[UltraMaXAtAXX]

"This is what separates the girls from the women."

[noablackdog]

@Ghaiyst did you really had a loo k at Euler's formula which is exactly:

e^'ix) = cos(x ) + i sin(x).

N.B. the method given in the video is nowhere near the simplest way to tackle with this indefinite integral; sufices to write that a primitive function of e^(-x) cos(x) is e(-x)( Acos(x) + Bsin(x)) and allyou need to do is equal derivates of both parts to get a simple linear system with A and B as unknown quantities...(takes less than 1 minute...)

[whizkid574]

Nobody else saw GOOD FOR MULTIFUC'N in the beginning!??!?

[potpie921]

Thank you for sharing!!

[NovaNixEternalFlame]

After you grasp the concept, this is easier and faster than integration by parts, and makes integrals with trigonometric functions relatively painless. I have no idea why they don't teach this everywhere...

[shawnwilliams77]

Fascinating...

[MrBigEnchilada]

dang this is such a cool way for integrating...forms of e^x * cosx or sinx

[MrBigEnchilada]

@jimztar lmao....

[Ghaiyst]

@hamsterpoop ooooooooooooh! ok thanks. i know a little bit about euler's method and the formula, but how that involves this problem makes complete sense! again thanks!