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Konform Afbildning og Dirichletproblemet

Kompleks Funktionsteori Eksempler c-10

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Language:  Danish
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Dette er den tiende bog med eksempler fra Kompleks Funktionsteori. Her gives eksempler på Konforme afbildninger, specielt homografier og den kvadratiske transformation samt eksponentialtransformationen. Der suppleres op med den vigtige Schwarz-Christoffel transformation. Videre gives nogle eksempler på Dirichletproblemet, dvs. et randværdiproblem for en elliptisk differentialligning, der ofte optræder i tekniske anvendelser. Specielt behandles Dirichletproblemet i øvre halvplan.

Selv om jeg har bestræbt mig på at være så omhyggelig som muligt, kan fejl ikke undgås, og da slet ikke i en første udgave. Jeg håber, at læseren kan vise forståelse herfor.

Leif Mejlbro
18. marts 2008

  1. Lidt supplerende teori
    1. Konform afbildning
    2. Homograer
    3. Specielle homograer
    4. Andre konforme afbildninger
    5. Schwarz-Christoels formel
    6. Dirichlet-problemet
  2. Konform afbildning
  3. Homograer
  4. Transformationen w = z2
  5. Eksponentialtransformationen w = exp z
  6. Schwarz-Christoels formel
  7. Dirichlet-problemet
  8. Specielle Dirichlet-problemer i vre halvplan
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.