Scenario

Sessions

 

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.