Conformal mapping and its applications

Bining Jia

doi:10.1117/12.2639473

17 May 2022 Conformal mapping and its applications

Bining Jia

Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 122591J (2022) https://doi.org/10.1117/12.2639473
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing, 2022, Kunming, China

Abstract

Conformal mapping is an important branch of complex analysis, which studies complex functions from a geometric point of view by mapping one region to another through an angle-preserved analytic function. It can simplify complex problems by mapping an irregular or complex domain to a regular or easier region. In this paper, we overview the definition of conformal mapping, the definition of linear fractional transformation, three well known automorphisms with conformal mapping and the history of Riemann mapping theorem. Besides, based on the Riemann mapping theorem, we study the Schwarz-Christoffel mapping from polygonal domains to the upper half plane or to the unit disk by giving the explicit construction of the conformal mapping. In addition, we also study the applications of conformal mapping on simplifying the Dirichlet problem by transforming Dirichlet problem in complex domains to Dirichlet problem in the unit disk, in which case the solution can be given by Poisson integral formula.

Citation Download Citation

Bining Jia "Conformal mapping and its applications", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 122591J (17 May 2022); https://doi.org/10.1117/12.2639473

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