Image:Exp series.gif

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Description

Illustration of the en:Exponential function

Source

self-made with MATLAB.

Date

Oleg Alexandrov 03:11, 30 August 2007 (UTC)

Author

Oleg Alexandrov

Permission
( Reusing this image)

see below



Public domain
I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


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MATLAB source code


% The exponential function as the sum of its Taylor series

function main()

   % KSmrq's colors
   red    = [0.867 0.06 0.14];
   blue   = [0, 129, 205]/256;
   green  = [0, 200,  70]/256;
   yellow = [254, 194,   0]/256;
   white = 0.99*[1, 1, 1];

% Set up the grid and other parameters
   N = 100;
   A = -3; B = 3; 
   X = linspace(A, B, N);
   Y = exp(X);
   D = max(Y); C = -0.2*D;
   

% plot the frames

   Sum = 0*X; Term = 0*X+1;
   num_frames = 8;
   for j=0:num_frames

      Sum = Sum+Term;
      Term = Term.*X/(j+1);

      % Set up the figure
      lw = 3; % linewidth
      fs = 20; % font size
      figure(1); clf; set(gca, 'fontsize', fs);
      hold on; grid on;
      set(gca, 'DataAspectRatio', [1 3 1]); % aspect ratio
      
      plot_axes (A, B, C, D, lw/1.3);

      plot(X, Sum, 'color', blue, 'linewidth', lw);
      plot(X, Y,   'color', red, 'linewidth', lw);

      axis([A, B, C, D]);
      
      text_str = sprintf('{\\it n}=%d', j)
      H= text (1.2, 18, text_str, 'fontsize', floor(1.2*fs))

      frame=sprintf('Frame%d.eps', 1000+j);
      disp(frame)
      saveas(gcf, frame, 'psc2');
         
   end

% Convert to animation with the command
% convert -antialias -loop 10000  -delay 100 -compress LZW Frame100* Exp_series.gif
   
   
function plot_axes (A, B, C, D, lw)
   
   black = [0, 0, 0];

   plot([A B], [0, 0], 'linewidth', lw, 'color', black);
   plot([0, 0], [C, D], 'linewidth', lw, 'colour', black);
   


File history

Click on a date/time to view the file as it appeared at that time.

Date/Time Dimensions User Comment
current 03:21, 30 August 2007 292×392 (51 KB) Oleg Alexandrov (tweak)
03:20, 30 August 2007 291×391 (50 KB) Oleg Alexandrov (tweak)
03:11, 30 August 2007 289×386 (49 KB) Oleg Alexandrov ({{Information |Description=Illustration of the en:Exponential function |Source=self-made with MATLAB. |Date=~~~~ |Author= Oleg Alexandrov }} Category:Calculus Category:Files by User:Oleg Alexandrov from en.wikipedia)
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