CONFORMAL MAPPING 2( Some Special Bilinear Transformations)

Bilinear Transformations, Mobius Transformation, Inverse Points and Fixed Points of Bilinear Transformation, Mappings
What you'll learn
Students will learn that under bilinear transformations, Circles or Straight Lines are mapped into Circles and Straight Lines and inverse points into inverse pt
To find the Bilinear Transformation that maps the region in z plane onto the region in w plane.
To find Most General Bilinear Transformation and its Mapping under given Conditions.
To Determine the Mobius Transformation and its Forms in accordance with the given Conditions.
How to Find the Images , Radius and Center of the Transformed Circle.
Requirements
Basic Knowledge of Complex numbers
Description
As Bilinear Transformation, Cross ratio, Fixed points, Normal form of Bilinear Transformations was alreday discussed in previous part. In this Course ' SOME SPECIAL BILINEAR TRANSFORMATIONS', Special emphasis will be given on finding the Bilinear Transformations or Mobius Transformations with Given Conditions.Contents of the Course Describes__Under the Bilinear Transformation, Circles and Straight lines are mapped into Circles and Straight lines and Inverse points are mapped into the Inverse points._How to calculate Inverse points._To find the Bilinear Transformation that maps Half Plane onto the Circular Disc in w plane along with Verification._To Find The General Transformation which maps half Plane onto the Unit Circular Disc and Unit Circular Disc onto Unit Circular Disc in w plane._Mapping of the Region in z plane to w Plane Conformally._Existence of Unique Function_To find the Mobius Transformation that maps the Circle in z plane onto the another circle in w plane conformally._To Determine the Most General Transformation that maps Unit Circle in z plane onto Unit Circle in w Plane._Mapping of Given Transformation from Real axis into Circle in w plane._Radius and Center of the Circle of the Transformed Circle and the transformed point in the center of the Circle in w Plane._How to get the Inverse Transformation from the Given Transformation._To Find the Bilinear Transformation that maps points in z plane to the points in w plane even for Concentric Circles._ Showing the Results to be Invariant under Given conditions_Expressing the given Relation in the form of bilinear Transformation._ including all Important Results and solved Assignments with Complete Explanation with Colorful Diagrams.
Who this course is for
Graduate Bsc. Students, MSc. mathematics students, Engineering and Physics Students, Post Graduate mathematical science students
Homepage

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