@matthewsheeran
Yep. Turns a complex (pun intended) integral into simple algebra for his students. Now that's a teacher!
@ShahzMunir
My favorite professor at MIT.
@gmortimer20031
Fair enough, I inhabit the complex domain, being a worker with signals, and so that would more-or-less be my way of doing it, although I would probably use the (to us) well-known identity cos( x ) = cosh( ix ) = ( exp( ix ) + exp( - ix )) / 2 :- I = integral( exp( -x ) cos( x ) dx ) substituting p = -x, we have dp = -dx exp(-x) = exp(p) cos(x) = cos(-x) = cos(p) Using the easily memorable identity cos( x ) = cosh( ix ) I = - integral( exp( p ) cosh( ip ) dp ) ( definition of cosh( x )) = -integral( exp(p)(( exp( ip ) + (exp(-ip))/2 ) ( defactoring ) = -1/2 x integral(exp((1+i)p) + exp((1-i)p ) ( integrating ) = -1/2 x (exp(1+i)p)/(1+i) + exp((1-i)p)/(1-i)) ( adding fractions ) = -1/2 x exp(p) * ((1-i)exp(ip) + (1+i)exp(-ip)) / ((1+i)(1-i)) ( expand and collect complex exponentials ) = -1/2 * exp( p ) x ( 2 cos(p) + 2 sin(p) ) / 2 ) (resubstituting p = -x ) = exp(-x)/2 x ( sin( x ) - cos( x ) ) no messing around with normalization or only considering real parts ( a possible source of doubt to the inquiring young mind ) needed.
@mikevaldez7684
Brilliant! Fantastic, straightforward exposition....beautiful. The internet really is a game changer 4 learning
@nareshmehndiratta
this is my second time seeing a lecture of Prof Arthur Mattuk after ten years
@jimztar
This is an awesome video, but you did forget the ' + c '
@canned_heat1444
Man, do I miss this course. Pure gold
@UltraMaXAtAXX
"This is what separates the girls from the women."
@hamsterpoop
@Ghaiyst Wikipedia: Euler's formula
@shadowmagician21
This guy is amazing
@gustavozapana3583
es una forma interesante de resolver con números imaginario porque usualmente lo resolvemos integración por partes pero una interesante clase en el prestigioso MIT saludos desde UNTELS LIMA PERU
@MrHamsi
thanks, that's definitely easier than integrating by parts!
@abaddon1112
if I had a chalkboard or dry erase board setup like that in my house, I'd have no use for video games.. only more chalk or dry erase markers lol
@quantummath
Damn it! it was just lovely.
@ryanchiang9587
diffetetial equations and partial differential equations are totally different!
@shawnwilliams77
Fascinating...
@Phatency
3:16 "Damn it.. this just always happens... well fuck it."
@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...)
@carsonb8952
integrating by parts seems way easier
@davidr6540