Step 1 :

Curves, Arcs, and Contours, and a definition of integration

We give vigorous analytic definitions of geometric entities like curves and arcs and define integration of a function of a complex variable and mention some of the natural integration properties.

Step 2:

Fundamental Theorem of Calculus

The student should be able to see clearly the extension of the Fundamental Theorem of Calculus from real analysis to complex analysis.

Step 3:

An equivalent definition of integration

We give an equivalent definition of integration suitable to derive a useful inequality.