Singularities of Analytic Functions -- Complex Analysis 20

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MathMajor

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The limit at 21:21 should be r->0, not r->infinity. Then M times a positive power of r (for negative n) goes to zero as required.

ingobojak

Nitpick about 22:30 (the second of the three equivalent statements): g isn't defined at z_0. Shouldn't we instead say that g has a removable singularity at z_0?

Jeff_Saunders

I just wanted to say that these course videos have been awesome. I haven't been able to keep up super well with the material during my term, but now that the summer is rolling around...

:)

TheEpicProOfMinecraf

21:40 r is less than R, so it shouldn't go to infinity. For n<0 the term M/r^n doesn't converge to 0 in my opinion when r tends to infinity 🤔

thomashoffmann

I hope we have a video on common meromorphic function examples. Not like exponential or trig functions, but weird functions like the Gamma function

JM-usfr

I'm a bit confused on the definition of isolated singularity. Wouldn't that make any point in an analytic function be an isolated singularity? Because, if a function is analytic and we just consider the point z_0 ( even if f is analytic on z_0), we can definitely find a punctured disk where f is also analytic. Or am I missing something? Does the fact that we are considering a punctured disk mean that we don't really care whether f is analytic on z_0 or not?

jimallysonnevado

Around 28:00
The preconditions of the theorem is maybe not enough. It has to be an isolated singularity which is not removable. Otherwise the limit doesn't need to be infinity (?)

thomashoffmann

30:32 It looks like Michael assumed that 1/|f(z)| has a isolated zero at z_0?

broccoloodle

Thank you for the awesome lessons/content!

Can we also expect to see a course on differential geometry?
I know I'd love to.
:)

Invalid

Convergence is dual to divergence.
Poles (eigenvalues) are dual to zeroes -- optimized control theory.
Analytic (mathematics) is dual to synthetic (physics) -- Immanuel Kant.
"Always two there are" -- Yoda.

hyperduality

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