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Sachin Kaushal, Lovely Professional University Unit 7: Transformations and Conformal Mappings

Unit 7: Transformations and Conformal Mappings Notes

CONTENTS
Objectives

Introduction
7.1 Transformations
7.1.1 Bilinear Transformation
7.1.2 Definitions
7.1.3 Transformation of a Circle

7.2 Conformal Mappings
7.2.1 Definition
7.3 Summary

7.4 Keywords
7.5 Self Assessment
7.6 Review Questions
7.7 Further Readings

Objectives

After studying this unit, you will be able to:
Define transformation

Discuss bilinear transformation

Describe transformation of a circle

Explain conformal mapping

Introduction

In earlier unit you have studied about concept of Cauchy's theorem, Cauchy's integral formula,
functions defined by integrals and maximum moduli. A conformal map is a function which
preserve angles. In the most common case, the function between domain is in the complex
plane. This unit will explain you the concept of transformation and conformal mapping.

7.1 Transformations

Here, we shall study how various curves and regions are mapped by elementary analytic function.
We shall work in  i.e. the extended complex plane. We start with the linear function.

w = Az (1)

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