Complex Analysis: Casorati Weierstrass Theorem (Intro)

Today, we introduce essential singularities and outline the Casorati-Weierstrass theorem. The proof of the theorem will be in the next video.

[douglasstrother]

exp(1/z) is the typical example in "Math Methods for Physics texts" of an essential singularity, then immediately avoided!

It's very fun to see the consequences of these beasts.

[mirriyaz]

Always pleasure to see your lectures . God bless you sir

[Alex_Deam]

Great Picard doesn't just say that f(z) attains every value bar one in any neighbourhood of the essential singularity - it says it attains all those values *infinitely many times* in those neighbourhoods. Which is mad. I hope to understand its proof one day too lol.

[contourintegral]

q chingados que grado es este? seguro no estado poniedo antencion en mi clase de matematicas

[theflaggeddragon]

Small correction. At a pole, it is not true that lim_{z->z_0}f(z) = infinty, rather lim_{z->z_0}|f(z)| = infinity. Indeed, the former already fails over R, where lim_{x->0}1/x does not exist since the left and right limits do not coincide. Great video btw!

[sunflower]

Physics building always have empty rooms :)

[Decrupt]

Looking forward to see the coming content on this. As always, it was a very fun and interesting to watch!

[pierreabbat]

What kind of singularity does cot(cot(z)) have at 0?

[navierstokes]

Which books do you like for an intro to complex analysis?

[mfourier]

i saw that theorem as any neighborhood V of z_0 essential singularitie satisfies that f(V) is dense, pretty cool theorem ^^

[peamutbubber]

How did you find it best to self study complex analysis