### Lecture 1: Properties of the Image of an Analytic Function: Introduction to the Picard Theorems

##### Lecture Details :

Advanced Complex Analysis - Part 2 by Dr. T.E. Venkata Balaji,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in

##### Course Description :

Theorems of Picard, Casorati-Weierstrass and Riemann on Removable Singularities:Properties of the Image of an Analytic Function:Introduction to the Picard Theorems,Recalling Singularities of Analytic Functions: Non-isolated and Isolated Removable, Pole and Essential Singularities,Recalling Riemann's Theorem on Removable Singularities,Casorati-Weierstrass Theorem; Dealing with the Point at Infinity -- Riemann Sphere and Riemann Stereographic Projection

Neighborhoods of Infinity, Limits at Infinity and Infinite Limits:Neighborhood of Infinity, Limit at Infinity and Infinity as an Isolated Singularity,Studying Infinity: Formulating Epsilon-Delta Definitions for Infinite Limits and Limits at Infinity

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