CONFORMAL MAPPINGS 1 (Complex Analysis)
Bilinear Transformations, Mobius Transformation, Fixed Points of Bilinear Transformation, Cross ratio of preservance
Ratings 0.00 / 5.00
What You Will Learn!
- Concept of Transformations or mapping from z plane to w plane.
- Concept of Standard or Elementary Transformations including Linear Transformation
- Bilinear or Linear Fractional Transformation including the concept of Mobius Transformations with all properties and examples.
- Elliptic, Parabolic, Hyperbolic and Loxodromic Transformation including Assignments based on it.
Description
A Conformal Mapping, also called a Conformal Map, Conformal Transformation, Angle-preserving transformation, or Biholomorphic map, is a transformation that preserves local angles.
The Course 'Conformal Transformations' describes about the mapping of points in the z plane to w plane including the other contents_
Detailed concept of Transformations and Jacobian of Transformation.
To determine the region in the w plane corresponding to the region given in z plane.
Necessary and Sufficient Condition for w = f(z) to represent Conformal Mapping.
Superficial magnification and Inverse points with respect to a Circle.
Some Elementary Transformation as Translation Transformation, Rotation Transformation, Magnification Transformation, Rotation and magnification Transformation, Inversion Transformation, Linear transformation.
Bilinear or Linear Fractional Transformation.
Determinant of Transformation and its Normalized Form.
Mobius Transformation and Critical Points.
Resultant or Product of Transformation.
Preservance of Cross ratio under bilinear Transformation
To Determine the Bilinear Transformation which maps the points in z plane to the points in w plane.
Steiner Circles and Family of circles.
Normal Form of Bilinear transformation and Fixed Points of Bilinear Transformation.
Every Bilinear Transformation transforms circles or straight lines into circles or straight lines and inverse points into inverse points.
Elliptical Transformation, Hyperbolic Transformation, Parabolic Transformation & Loxodromic Transformation including all expected solved examples and Important Theorems.
Who Should Attend!
- This Course is a basic course offered to Undergraduate or Post Graduate Students of Engineering and Science background.