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Complex Functions Examples c-3

Elementary Analytic Functions and Harmonic Functions

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Language:  English
This is the third textbook containing examples from the Theory of Complex Functions.
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Description
Preface
Content

This is the third textbook containing examples from the Theory of Complex Functions. Some of the topics are examples of elementary analytic functions, like polynomials, fractional functions, exponential functions and the trigonometric and the hyperbolic functions.

This book requires knowledge of Calculus 1 and Calculus 2.

This is the third book containing examples from the Theory of Complex Functions. The first topic will be examples of elementary analytic functions, like polynomials, fractional functions, exponential functions and the trigonometric and the hyperbolic functions. Then follow some examples of harmonic functions.

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

4th June 2008

  1. Some necessary theoretical results
  2. Polynomials
  3. Fractional functions
  4. The exponential function and the logarithm function
  5. Trigonometric and hyperbolic functions
  6. Harmonic functions
About the Author

Leif Mejlbro

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.