Step 1:
Look at the history of complex numbers
The student
will see how complex numbers were constructed in a natural
way.
Step 2:
Examine the calculus
We look at not
only the basic operations dealing with complex numbers,
but also other operations like taking square roots, the
triangle inequality, and the like.
Step 3:
Generalize from real to complex
functions
Since the set of
real numbers is a subset of complex numbers, it is natural
to explore how different concepts from real analysis
extend to complex analysis.
Step 4:
Look at different function
characteristics
We discuss
limits of functions, continuous, differentiable and
holomorphic functions and their relationships. |