Scenario

Sessions

 
 

Step 1 :

Complex Analysis cannot be studied without knowing basic topology

We introduce the basic definitions and concepts from topology especially on the set of complex numbers

Step 2:

More topology in C

The next step is to study deeper topological concepts like completeness of R and its positive impact on the completeness of C.  Other concepts include compactness and connectedness.

Step 3:

Convergence (pointwise) and uniform convergence

Here we turn to the important issues of convergence and how uniform convergence facilitates doing the things that we would like to do like term-by-term integration and term-by-term differentiation provided that we stay within the disk of convergence.