Section21.6

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## 21.6 images7.input

First we look at the conformal conformal map map z↦z+1/z.

)read conformal Read program for drawing
conformal maps
f z == z The coordinate grid for the
complex plane
conformalDraw(f, -2..2, -2..2, 9, 9, "cartesian") Mapping 1: Source
f z == z + 1/z The map z↦z+1/z
conformalDraw(f, -2..2, -2..2, 9, 9, "cartesian") Mapping 1: Target

The map z↦-(z+1)/(z-1) maps the unit disk to the right half-plane, as shown Riemann:sphere on the Riemann sphere.

f z == z The unit disk
riemannConformalDraw(f,0.1..0.99,0..2*%pi,7,11,"polar") Mapping 2: Source
f z == -(z+1)/(z-1) The map x↦-(z+1)/(z-1)
riemannConformalDraw(f,0.1..0.99,0..2*%pi,7,11,"polar") Mapping 2: Target
riemannSphereDraw(-4..4, -4..4, 7, 7, "cartesian") Riemann Sphere Mapping
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