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Stability, Riemann Surfaces, Conformal Mappings

Complex Functions Theory a-3

Stability, Riemann Surfaces, Conformal Mappings
3.6 (17 reviews)
ISBN: 978-87-7681-702-2
1 edition
Pages : 115
  • Price: 129.00 kr
  • Price: €13.99
  • Price: £13.99
  • Price: ₹250
  • Price: $13.99
  • Price: 129.00 kr
  • Price: 129.00 kr

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About the book

  1. Description
  2. Content
  3. About the Author

Description

This Complex Functions Theory a-3 text is the third e-book in a series which has previously characterized analytic functions by their complex differentiability and proved Cauchy’s Integral Theorem, as well as provided alternative proofs which show that locally, every analytic function is described by its Taylor series. Complex Functions Theory a-3 builds on these previous texts and collects related applications, proving the argument principal, introducing criteria of stability in dynamic systems, visualizing many-valued functions through their corresponding Riemann surfaces, and elegantly solving some Dirichlet problems. This e-book and previous titles in the series can be downloaded for free here. All theorems are accompanied by their proofs, and all equations are explained and demonstrated in detail. A comprehensive index follows the text.

Readers interested in a full overview of complex analytic functions should refer to the related titles in this series, all of which are available for free download on bookboon.com: Elementary Analytic Functions - Complex Functions Theory a-1, Calculus of Residua - Complex Functions Theory a-2, and The Laplace Transformation I – General Theory - Complex Functions Theory a-4.

Content

  1. The argument principle, and criteria of stability
  2. Many-valued functions and Riemann surfaces
  3. Conformal mappings and the Dirichlet problem
  4. Index

About the Author

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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