CONFORMAL MAPPING 2( Some Special Bilinear Transformations)
Bilinear Transformations, Mobius Transformation, Inverse Points and Fixed Points of Bilinear Transformation, Mappings
Ratings 0.00 / 5.00
What You Will 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.
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 Should Attend!
- Graduate Bsc. Students, MSc. mathematics students, Engineering and Physics Students, Post Graduate mathematical science students