Laurent Series Explained | How to Determine Laurent Series | Complex Analysis #9

Everything you need to know about Laurent Series explained! This video covers the definition, properties, and practical problems on how to determine all possible Laurent Series for a complex function, focusing on the techniques for each region.

✨ In this lesson, you'll learn:
► The definition of a Laurent Series, including its principal and analytic parts.
► How to determine all possible Laurent Series around a point of expansion.
► How the region of convergence (annulus domain) dictates the form of the series.
► Practical methods for solving Laurent Series problems, often using geometric series.

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📚 Resources & Playlists
Full Complex Analysis Course:    • Complex Analysis Explained (Full Course)  
Download the Lecture Notes: https://drive.google.com/file/d/1IHef...

🔑 Key Concepts & Theorems
Laurent Series
Principal Part
Analytic Part
Annulus Domain
Isolated Singularity
Geometric Series

🔖 Chapters
00:00 Intro
00:13 Theorem: Laurent Series
01:06 What is an Annulus Domain?
02:04 Good Things to Know (Residue, Taylor Series relation, Convergence)
03:40 Why Geometric Series are Best
05:20 Example 1: f(z) = 1/(z-2) around z=0
08:02 Example 2: f(z) = 1/(z-2) around z=1
09:48 Example 3: f(z) = 1/((z-1)(z-2)) around z=0
13:40 Outro

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