Ali Hassan Mohamed Murid
UTM Centre for Industrial and Applied Mathematics, Institute for Scientific and Industrial Research, Universiti Teknologi Malaysia, Johor Bahru
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Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru

CONFORMAL MAPPING, BOUNDARY VALUE PROBLEMS, FLUID FLOW, AND IMAGE PROCESSING

A two-dimensional mapping with the property that angles between curves are preserved in magnitude as well as in direction is called a conformal mapping. Conformal mapping has been an important tool of science and engineering since the development of complex analysis. A conformal mapping uses functions of complex variables to transform a complicated boundary to a simpler, more manageable configuration. In various applied problems, by means of conformal maps, problems for certain “physical regions” are transplanted into problems on some standardized “model regions” where they can be solved easily. By transplanting back we obtain the solutions of the original problems in the physical regions. This process is used, for example, for solving problems about fluid flow, electrostatics, and aerodynamics. This talk will give an integral equation method for constructing conformal maps. Recent applications of conformal maps in fluid flow, void defect detection, and image processing will be discussed.