Exp8_1.m

clc; clear; close all;                    
syms x y z
T = 100 - x^2 - y^2 - z^2;                 
F = gradient(T, [x y z]);  
disp('gradF='); disp(F.');
[X, Y, Z] = meshgrid(-4:2:4);              % grid from -4 to 4 with step 2 in each coordinate
Ux = double(subs(F(1), {x, y, z}, {X, Y, Z}));  % numeric array for x-component of gradient
Uy = double(subs(F(2), {x, y, z}, {X, Y, Z}));  % numeric array for y-component of gradient
Uz = double(subs(F(3), {x, y, z}, {X, Y, Z}));  % numeric array for z-component of gradient
quiver3(X, Y, Z, Ux, Uy, Uz, 'LineWidth', 1);
axis equal; grid on;                        % equal axis scaling and grid
title('Gradient Vector Field T'); % title (shows the gradient symbol)
xlabel('X-axis');                                % label x-axis
ylabel('Y-axis');                                % label y-axis
zlabel('Z-axis');                                % label z-axis