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Plot graphs using Mathematica

by raghavendar24
Tags: graphs, mathematica, plot
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raghavendar24
#1
Aug21-09, 03:04 AM
P: 9
hi ,


i am unable to draw the graphs of complex valued functions using mathematica,

please help me .

Ex:koebe function. z/(1-z)^2, z is a complex number
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DaleSpam
#2
Aug21-09, 06:55 AM
Mentor
P: 17,322
How do you want to display the function? One common approach is to use ContourPlot and plot the Abs as the contours and use Arg for the colors.
raghavendar24
#3
Aug21-09, 07:12 AM
P: 9
Hi, thnx for reply, please say how to plot in two ways so that i can use which is is required for me, and other one i may use whenever i needed.

Thank you.

DaleSpam
#4
Aug21-09, 07:47 PM
Mentor
P: 17,322
Plot graphs using Mathematica

ParametricPlot[
Through[{Re, Im}[(x + I y)/(1 - (x + I y))^2]], {x, 0, 2}, {y, -1,
1}, PlotRange -> {-1, 1}]


Plot3D[Abs[(x + I y)/(1 - (x + I y))^2], {x, 0, 2}, {y, -1, 1},
ColorFunction ->
Function[{x, y},
Hue[Arg[(x + I y)/(1 - (x + I y))^2]/(2 \[Pi]) + .5]],
ColorFunctionScaling -> False]
raghavendar24
#5
Aug24-09, 12:45 AM
P: 9
Thank you so much.



Can you suggest me any book which is useful to plot this type of functions using mathematica
raghavendar24
#6
Aug24-09, 03:40 AM
P: 9
Hi one more doubt regarding the above problem,

The function z/(1-z)^2 maps the unit disk |z|<1 onto the entire plane except a line segment

from (-infinity to -1/4) , how can we show that using the above function plot using mathematica.

Thanking you
DaleSpam
#7
Aug24-09, 11:18 AM
Mentor
P: 17,322
Quote Quote by raghavendar24 View Post
Can you suggest me any book which is useful to plot this type of functions using mathematica
I have found the online help (F1) to be quite thorough.

Quote Quote by raghavendar24 View Post
Hi one more doubt regarding the above problem,

The function z/(1-z)^2 maps the unit disk |z|<1 onto the entire plane except a line segment

from (-infinity to -1/4) , how can we show that using the above function plot using mathematica.
Use the parametric plot version shown above, but map the complex plane using r Exp[-I theta] instead of x + I y
raghavendar24
#8
Aug24-09, 11:32 AM
P: 9
I already work out at that time i have some doubt whether it is right or not, thank you now i conformed but here is a problem i m unable to interpret from the figure it mapping the unit disk

that is |z|<1 (in polar form we are using r Exp(I*theta)


r varies from 0 to 1

and theta varies from 0 to 2 pi )


to the entire XY plane except a line segment
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DaleSpam
#9
Aug24-09, 02:02 PM
Mentor
P: 17,322
Yes, that looks correct.


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