Plot graphs using Mathematica

  • Mathematica
  • Thread starter raghavendar24
  • Start date
  • #1
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
 

Answers and Replies

  • #2
Dale
Mentor
Insights Author
2020 Award
31,312
8,097
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.
 
  • #3
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.
 
  • #4
Dale
Mentor
Insights Author
2020 Award
31,312
8,097
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]
 
  • #5
Thank you so much.



Can you suggest me any book which is useful to plot this type of functions using mathematica
 
  • #6
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
 
  • #7
Dale
Mentor
Insights Author
2020 Award
31,312
8,097
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.

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
 
  • #8
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
 

Attachments

  • Untitled-1.pdf
    137.2 KB · Views: 194
  • #9
Dale
Mentor
Insights Author
2020 Award
31,312
8,097
Yes, that looks correct.
 

Related Threads on Plot graphs using Mathematica

Replies
1
Views
4K
Replies
1
Views
10K
Replies
2
Views
977
Replies
1
Views
6K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
3K
Replies
1
Views
4K
Replies
1
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Top