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. |