In this Section we consider two important features of complex functions. The Cauchy-Riemann equations provide a necessary and sufficient condition for a function to be analytic in some region of the complex plane; this allows us to find in that region by the rules of the previous Section.
A mapping between the -plane and the -plane is said to be conformal if the angle between two intersecting curves in the -plane is equal to the angle between their mappings in the -plane. Such a mapping has widespread uses in solving problems in fluid flow and electromagnetics, for example, where the given problem geometry is somewhat complicated.
- understand the idea of a complex function and its derivative
- use the Cauchy-Riemann equations to obtain the derivative of complex functions
- appreciate the idea of a conformal mapping
1.1 Analytic functions and harmonic functions
2 Conformal mapping
2.1 Function as mapping