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CONFORMAL MAPPING 2 Bilinear Transformations
15 students

CONFORMAL MAPPING 2 Bilinear Transformations

Bilinear Transformations, Mobius Transformation, conformal mapping, complex analysis, msc mathematics, mappings
Created byJaswinder Kaur
Last updated 5/2026
English

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.

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Course content

3 sections • 17 lectures • 3h 14m total length

  • Introduction of mapping of Bilinear Transformation and the Inverse Points4:29
  • To Find all Bilinear Transformations which maps half plane I(z)>=0 onto |w| <=113:01
  • Find the General Bilinear Transf. that maps R(z)>=0 onto Unit Circular Disc .12:47
  • Find the General Bilinear Transf. that maps |z|<=1 onto |w|<= 117:20
  • Find the General bilinear Transf. that maps |z-z0|<= R onto |w|<= 114:35

Requirements

  • Basic Knowledge of Complex numbers

Description

The previous part discussed bilinear transformations, cross-ratio, fixed points, and the normal form of bilinear transformations. In this Course,' SOME SPECIAL BILINEAR TRANSFORMATIONS,' special emphasis will be given to finding 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 the w plane along with Verification.

  • To Find The General Transformation that maps the half-plane onto the Unit Circular Disc and the Unit Circular Disc onto the Unit Circular Disc in the w-plane.

  • Mapping of the Region in the z plane to the w Plane Conformally.

  • Existence of a Unique Function

  • To find the Mobius Transformation that maps the Circle in the z plane onto another circle in the w plane conformally.

  • To determine the Most General Transformation that maps the Unit Circle in the z-plane onto the Unit Circle in the w-plane.

  • Mapping of Given Transformation from Real axis into Circle in w plane.

  • The radius and Center of the Transformed Circle and the transformed point in the center of the Circle in the w Plane are shown.

  • 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 a bilinear Transformation.

  • Including all critical results and solved assignments, with complete Explanations and 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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