Taylor Series Explained | Solving Taylor Series with Geometric Series | Complex Analysis #8 скачать в хорошем качестве

Taylor Series Explained | Solving Taylor Series with Geometric Series | Complex Analysis #8

Learn how to determine the Taylor Series for complex functions, even around tricky points! This video focuses on using the geometric series (1/(1-z)) as a powerful tool and explains how to find the Taylor Series radius of convergence. ✨ In this lesson, you'll learn: ► The definition of a Taylor Series for complex functions. ► How to utilize the geometric series for Taylor Series expansion. ► How to determine the radius of convergence for a Taylor Series. ► The fundamental relationship between analytic functions and Taylor Series. ☕ Support the Channel If you found this video helpful and would like to support the creation of more free math lessons, please consider buying me a coffee! It helps me turn this into a full-time job. ko-fi.com/themathcoach 📚 Resources & Playlists Full Complex Analysis Course:    • Complex Analysis Explained (Full Course)   Download the Lecture Notes: https://drive.google.com/file/d/0B0vT... 🔑 Key Concepts & Theorems Taylor Series Geometric Series (1/(1-w)) Radius of Convergence Analytic Functions Poles Partial Fraction Decomposition 🔖 Chapters 00:00 Definition Taylor Series 00:15 Theorem Taylor Series 00:35 Definition Radius of Convergence 00:59 Example 1: f(z) = 1/(2+z) around z=0 01:30 Example 2: f(z) = 1/(2+z) around z=1 04:23 Example 3: f(z) = -1/(2+z)^2 around z=1 05:42 Example 4: f(z) = (z-2)/((z+2)(z+3)) around z=0 07:03 Outro 🔔 Subscribe & Ask Questions If this video helped you understand the subject, please like and subscribe! Have a question about Taylor series or radius of convergence? Ask away in the comments below! I read every comment and will do my best to help you understand the concepts better. #TheMathCoach #ComplexAnalysis #TaylorSeries #PowerSeries #GeometricSeries #Mathematics #UniversityMath