Image:Exp series.gif

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[edit] 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, 'color', black);
   

• Exponential function
• Taylor series
• Power series