December 2020
Intermediate to advanced
1064 pages
49h 43m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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20.2 Conformal Mappings
INTRODUCTION
In Section 20.1 we saw that a nonconstant linear mapping f(z) = az + b, a and b complex numbers, acts by rotating, magnifying, and translating points in the complex plane. As a result, it is easily shown that the angle between any two intersecting curves in the z-plane is equal to the angle between the images of the arcs in the w-plane under a linear mapping. Other complex mappings that have this angle-preserving property are the subject of our study in this section.
Angle-Preserving Mappings
A complex mapping w = f(z) defined on a domain D is called conformal at z = z0 in D when f preserves the angles ...