In the previous set of notes we introduced the notion of a *complex diffeomorphism* between two open subsets of the complex plane (or more generally, two Riemann surfaces): an invertible holomorphic map whose inverse was also holomorphic. 13,203 more words

## Tags » Conformal Mapping

#### 246A, Notes 5: conformal mapping

#### Visualizing Complex Functions with Conformal Mapping

For the thoroughly modern calculus student, an introduction to Complex Variables is all the more daunting because we don’t have the kind of geometric intuition-building machinery available to us for functions as we did for real-valued functions in calculus. 202 more words

#### Complex Mathematics - Integral using Residue Theorem, Conformal Mapping

Guys,

In complex analysis, the residue theorem, sometimes called Cauchy’s residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals as well. 63 more words

#### Conformal Mapping

In a previous post I explored complex functions through domain coloring. Here I would like to explore another element of complex functions – conformal mapping. The idea here is to consider some curve in the complex plane, and apply a function to it, and see what happens. 568 more words