Introduction

The transformation w = iz + i

The transformation w = (3-4i)z+6+2i

The transformation w = (-1+i)z - 2+3i

The mapping w = z²

The mapping w = z²

The mapping w = z^1/2

Branches of the square root.

The transformation w = exp(z)

The fundamental period strip for the mapping w = exp(z)

Image of a rectangle under the mapping w = exp(z)

The single-valued mapping w = Log(z)

A branch of w = Log(z)

The mapping w = (e^z-i)/(e^z+i)

The mapping w = Log[(1+z)/(1-z)]

The mapping w = tan(z)

The mapping w = sin(z)

The mapping w = arcsin(z)

Other topics illustrated with the software F(Z)

Conformal Mappings

The Mobius Transformation

The Dirichlet Problem

Steady State Temperatures

Two-Dimensional Electrostatics

Two-Dimensional Ideal Fluid Flow

The Schwarz-Christoffel Transformation

Sources and Sinks in Two Dimensions

Julia and Mandelbrot Sets

Complimentary software to accompany the text

COMPLEX ANALYSIS: for Mathematics and Engineering

(c) John Mathews, 1998