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Complex Functions Examples c-9

The Argument Principle and Many-valued Functions

Complex Functions Examples c-9
4,7 (16 Bewertungen)
ISBN: 978-87-7681-395-6
1. Auflage
Seiten : 121
Preis: Kostenlos

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Beschreibung

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

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Über das Buch

  1. Beschreibung
  2. Einleitung
  3. Inhalt
  4. Über den Autor

Beschreibung

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.

Einleitung

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

Inhalt

Introduction

1. Some theoretical background
1.1 The argument principle
1.2 Stability criteria
1.3 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

Über den Autor

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 his retirement in 2003. He has twice been on leave, first time one year at the Swedish Academy, Stockholm, and second time at the Copenhagen Telephone Company, now part of the Danish Telecommunication Company, in both places doing research.

At the Technical University of Denmark he has during more than three decades given lectures in such various mathematical subjects as Elementary Calculus, Complex Functions Theory, Functional Analysis, Laplace Transform, Special Functions, Probability Theory and Distribution Theory, as well as some courses where Calculus and various Engineering Sciences were merged into a bigger course, where the lecturers had to cooperate in spite of their different background. He has written textbooks to many of the above courses.

His research in Measure Theory and Complex Functions Theory is too advanced to be of interest for more than just a few specialist, so it is not mentioned here. It must, however, be admitted that the philosophy of Measure Theory has deeply in uenced his thinking also in all the other mathematical topics mentioned above.

After he retired he has been working as a consultant for engineering companies { at the latest for the Femern Belt Consortium, setting up some models for chloride penetration into concrete and giving some easy solution procedures for these models which can be applied straightforward without being an expert in Mathematics. Also, he has written a series of books on some of the topics mentioned above for the publisher Ventus/Bookboon.

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