clc
close all
clear all

% first exercise of the day
figure
X = -6:.1:6;
Y = -6:.1:6;
[x, y] = meshgrid(X, Y);
z = 6 - 2*x.^2 - 4*y.^2;
mesh(x, y, z)
xlabel('x')
ylabel('y')
zlabel('z')

% second exercise of the day
figure
z = @(x, y) log(x) -2*x.^2 + y.^4 - 32*y; % log is the natural logarithm
% Use log10() for the decimal logarithm
fsurf(z, [0, 6, -6 6])
xlabel('x')
ylabel('y')
zlabel('z')

% third exercise of the day
figure
hold on
I = [0, 2, 0 2]
fsurf(@(x, y) x.^2*y.^3, I)
xlabel('x')
ylabel('y')
zlabel('z')
T0 = @(x, y) 1 + 0*x + 0*y;
fsurf(T0, I)
T1 = @(x, y) 1 + 2*(x - 1) + 3*(y - 1);
fsurf(T1, I)
T2 = @(x, y) 1 + 2*(x - 1) + 3*(y - 1) + (x - 1).^2 + ...
    6*(x - 1)*(y - 1) + 3*(y - 1).^2;
fsurf(T2, I)