Introduction
Target audience :
This course is designed for fourth-year students MST & SST of the Higher Teachers Training School.
Author :
It was produced by Dr. Aitemrar Chafika Amel.
Description :
This course is about the conformal transformations, also called conformal maps, they are transformations that preserve local angles. An analytic function is conformal at any point where it has a nonzero derivative. Conversely any conformal mapping of a complex variable which has continuous partial derivatives is analytic. Conformal mapping is extremely important in Complex analysis, as well as in many areas of physics and engineering.
Course aims :
The aim of this course is to study the conformal transformations, first we will look at the geometric notions of conformal maps. It will turn out that analytic functions are automatically conformal. Once we have understood the general notion, we will look at the specific family of conformal maps called fractional linear transformations and, in particular at their geometric properties.
Near required :
Students need basic knowledge of the following modules : Algebra, Geometry, Complex analysis.