% btm_fig77 generates a contour and "quiver" plot of the temperature
%  T(x,y) and its gradient, approximating figure 7.7 in "Basic
%  Training in Mathematics" by R. Shankar.
% 
% The function is T(x,y) = y^2 + x^2.

% Programmer: Dick Furnstahl  furnstahl.1@osu.edu
%
% Revision history:
%   01-May-2005 -- original version for Physics 263
%

clear;    % this sets variables to zero, so we start with a clean slate

% Set a grid X Y with the desired range (and gridsize points on each axis)
xmin = -2;  xmax = 2;   % set the minimum and maximum values of x
ymin = -2;  ymax = 2;   % set the minimum and maximum values of y
gridsize = 20;
[X Y] = meshgrid( linspace(xmin,xmax,gridsize), linspace(ymin,ymax,gridsize) );

T = Y.^2 - X.^2;   % define the temperature function

[Tx Ty] = gradient(T);  % calculate the gradient with the x-component
                        %  stored in Tx and the y-component in Ty

% Draw the figure (we use "hold" to let us draw two plots on one figure)
figure(1);                               % figure 1 will be a contour plot
num_contours = 6;                        % use num_contours contour lines
contourf(X,Y,T,num_contours); colorbar;  % make the plot and add a color bar
hold on;                                 % hold the current plot
scale = 1;                               % scaling of vector lengths
quiver(X,Y,Tx,Ty,scale);                 % plot the gradient vectors
xlabel('x-axis');  ylabel('y-axis');     % add labels
hold off;                                % release the hold