Evaluating Real Integrals With Cauchy's Residue Theorem - Complex Analysis By A Physicist

In this video we go over what is one of the most important and useful applications of Cauchy's Residue Theorem, evaluating real integrals with Residue Theorem. This may seem a bit confusing. How can we evaluate a real integral with a complex analysis theorem? The answer is very interesting and opens up the ability to evaluate many different kinds of integrals via analytic means.

Music: Mirror Mind By Bobby Richards

[palesadhlamini]

WOW YOU JUST HELPED ME TO PREPARE FOR MY EXAMS.EVERYTHING NOW MAKES SENSE

[keithphw]

Love your applications, commentary and intuition. Thanks for the great videos!

[davethesid]

Very helpful, thank you! Bounding the integral on the upper arc of the semicircle to show that it goes to 0 in the limit takes some extra work, though.

[Julie-slqs]

At 8.39 how do you get to those functions in the limit?

[emrekt]

thank you very much for the videos, really helpful

[ayeshaghafoor]

What about the convergence or real integral in the disk where we convert and integrate? If real integral doesn't convergence in the disk, it's impossible to do next steps.

[neal]

this integrals so nasty when my mom get in to the room i had to close the computer

[zlatanbrekke]

Why does this only work for -∞ and ∞ ? If the boundaries is -10 and 10 we will get the same singularity in ∂R not the same answer…

[korayozdemir]

why can you say cosz=real part of e^iz? if you solve directly for cos z, the answer will be the same?

[hyperduality]

Real is dual to imaginary -- complex numbers are dual.
"Always two there are" -- Yoda.