Types of Isolated Singularities - Complex Analysis By a Physicist

In this video we cover isolated singularities, and the three types of isolated singularities. The three kinds of isolated singularities covered are poles, essential singularities, and removeable singularities.
Understanding isolated singularities relies heavily on Laurent series.
You can refresh you memory on Laurent series here:

Music: Mirror Mind By Bobby Richards

[tariqandrea]

It is a sad commentary on the world's top universities when a 5-minute video from a thoughtful instructor accomplishes what most of these venerable institutions miserably fail to do. Yes indeed from Stanford, to Berkeley, University of Toronto and all the rest.

[rachiekimberly]

How did u explain it better in a 5 minute video than my lecturer did in a 2 hour lecture? haha

[dhanya]

Another way to interpret this is that
* Finite number of principal parts( negative powere of z) in the Laurent' s expansion- Pole.
*Infinite number of principal parts in the Laurents expansion -Essential singularity.
* Only positive powers of z in the expansion - removable singularity.
All these expansions are about the singular point meaning ur expansion should be of the form(z-z0).if z0 is the singularity.

[kowalski]

hey for e^1/z the expansion might be wrong, I've checked some sources and they state that there is a factorial multiplied with each Z.

[prayashbhuyan]

Can somebody show the Laurent expansion of z^3/2-z

[goodlearnerbadstudent]

At 2:33, how did you get the expansion shown? I am not sure what series is it supposed to look like?

I tried watching your other video about Laurent Series but I am still unsure how this function should be expanded.

But your explanation of the singularities was very intuitive.
Thank you!

[marinestanley]

i have gone through so many of these videos, this is the first time I understand. Great explanation

[Lord-kdee]

Can you explain how you expanded z³/(2-z) ? I know how to do it in z=0, but can't figure out how to do it in z=2