Power series 1: Radius of Convergence

Описание: We motivate the power series by looking for a function f whose derivative is itself. Also, the Taylor series of an infinitely differentiable function. We prove a result on the radius of convergence of a power series. The proof is different from the standard ones found in textbooks which use the Hadamard's formula for the radius of convergence.

Timestamp provided by Ishwarya.
00:00 Introduction
0:43 Goal of this lecture series
2:04 Motivation of power series: Look for a function whose derivative is itself
6:45 Taylor's series of an infinitely differentiable function (In real variable)
14:47 Power series in complex analysis
18:17 Examples
22:50 Fact: An important fact about convergent power series
25:16 Power series centered at a in C
26:04 Theorem about Radius of convergence & its proof
33:44 Conclusion