Complex Functions Examples c-9

This is the ninth book containing examples from the Theory of Complex Functions. We shall here treat the important Argument Principle, which e.g. is applied in connection with Criteria of Stability in Cybernetics. Finally, we shall also consider the Many-valued functions and their pitfalls.

Even if I have tried to be careful about this text, it is impossible to avoid errors, in particular in the first edition. It is my hope that the reader will show some understanding of my situation.

Leif Mejlbro

27th June 2008

1. Some theoretical background
   1. The argument principle
   2. Stability criteria
   3. Inverse functions
2. The argument variation
3. Stability criteria
4. The innitely-valued function log z
5. The many-valued functions az and za
6. The Arcus Functions and the Area Functions
7. The inverse of an algebraic expression
8. Simple example of potential flows