File:Maximum modulus principle.png

Summary

Description
English: Illustration of Maximum modulus principle
Date
Source Own work
Author Oleg Alexandrov
PNG development
InfoField

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Category:Self-published work#Maximum%20modulus%20principle.pngCategory:PD-self#Maximum%20modulus%20principle.png

Source code (MATLAB)

 

function main()

   % the number of data points. More points means prettier picture.
   N = 50;

   RR=linspace(0, 1, N);
   TTheta = linspace(-pi, pi, N);

   [R, Theta] = meshgrid(RR, TTheta);

   I=sqrt(-1);
   Z = R.*exp(I*Theta);
   X = real(Z); Y = imag(Z);
   
   FZ = cos(Z);
   AFZ = abs(FZ);
   
   figure(1); clf; hold on; axis equal; axis off;

   surf(X, Y, AFZ, 'FaceColor',    'red', 'EdgeColor','none', 'FaceAlpha', 1);
   surf(X, Y, 0*AFZ, 'FaceColor', 'blue', 'EdgeColor','none', 'FaceAlpha', 0.5); 

% add in two sources of light
   camlight (50, 54); 
   camlight (50, -20);
   lighting phong;

% viewing angle
   view(149, 22);

% save as png
  print('-dpng', '-r200', 'Maximum_modulus_principle.png');
Category:Complex analysis Category:Files by User:Oleg Alexandrov from en.wikipedia Category:Images with MATLAB source code Category:Surface plots of complex functions
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Category:Math images that should use vector graphics#%20Maximum%20modulus%20principle.pngCategory:PNG that should use vector graphics
Category:Complex analysis Category:Files by User:Oleg Alexandrov from en.wikipedia Category:Images with MATLAB source code Category:Math images that should use vector graphics Category:PD-self Category:PNG created with MATLAB Category:PNG that should use vector graphics Category:Self-published work Category:Surface plots of complex functions