Complex Analysis 3: Holomorphic Functions - 1

We define thee differentiability of a function from C to C. We introduce the notion of holomorphic and entire functions. We state and prove a simple characterization of differentiability and use it to show that the set of functions differentiable at a point form a complex vector space. A few simple examples of differentiable functions are given.

Timestamp provided by Ishwarya.

0:00 Introduction
0:44 Motivation for the Lecture
2:20 Differentiability of a complex function of a complex variable
5:14 Holomorphic function
6:52 Basic Examples
10:02 Characterization of a differentiability
16:59 Trick to find f1
20:20 Algebra of Differentiable functions
31:59 More examples
37:53 Entire function & examples
44:30 Conclusion

[surjyanarayanrath]

🙏Sir...

Really your characterisation on differentiability is awesome.

[rinkubharali]

Sir with honour, most of the time I have seen in Lectures in Higher Mathematics contains only . Professor don't focus on *Problem Solving* . So a natural Question arises, is studying Higher Mathematics is more about understanding the Concepts/Ideas/Notions which is developed before us and less about *Problem Solving* . Honestly what do you have to say about it?