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



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