The Argument Principle and Many-valued Functions

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121 pages

Språk:

English

This is the ninth textbook you can download containing examples from the Theory of Complex Functions.

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Om forfatteren

*Leif Mejlbro* was educated as a mathematician at the *University of Copenhagen*, where he wrote his thesis on *Linear Partial Differential Operators and Distributions*. Shortly after he obtained a position at the *Technical University of Denmark*, where he remained until h...

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Content

This is the ninth textbook you can download 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.

This book requires knowledge of Calculus 1 and Calculus 2.

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

- Some theoretical background
- The argument principle
- Stability criteria
- Inverse functions

- The argument variation
- Stability criteria
- The innitely-valued function log z
- The many-valued functions az and za
- The Arcus Functions and the Area Functions
- The inverse of an algebraic expression
- Simple example of potential flows