9 Analytic Functions #analyticfunction

In this lecture, we introduce and explore the concept of analytic functions, a central idea in complex analysis. We begin by defining what it means for a function to be analytic at a point and analytic in an open set. The discussion then progresses to highlight how analyticity is a stronger condition than mere differentiability.

We illustrate these concepts through carefully selected examples and highlight the criteria for non-analyticity, particularly using the Cauchy-Riemann equations. We also present a sufficient condition for analyticity and discuss under what circumstances an analytic function must be constant.

🧠 Topics Covered:
✅ Definition of analytic functions (at a point and in an open set)
✅ Analyticity vs. Differentiability
✅ Examples demonstrating the importance of analyticity
✅ Using Cauchy-Riemann equations to test non-analyticity
✅ Sufficient conditions for a function to be analytic
✅ When an analytic function becomes constant

🎯 Best For:
– B.Sc. & M.Sc. Mathematics students
– B.Tech. Engineering Mathematics students
– Competitive exam prep: CSIR-NET, GATE, IIT-JAM, etc.
– Anyone studying or revising Complex Analysis

📘 Watch Complete Complex Analysis Series: https://www.youtube.com/playlist?list=PLzt330quwYmWpY2BQMFeSxSpeZnv7LJt-
🔗 Lecture Playlist

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