clc
close all
clear all

%% EXERCISE 1
disp("************ EXERCISE 1 ************")
M = 1000;
ii = .1;
R1 = M/((1 + .5*ii)*(1 + ii)^.5);
fprintf("R1 = %.3f\n", R1)
R2 = M/(1 + ii);
fprintf("R2 = %.3f\n", R2)

%% EXERCISE 2
disp("************ EXERCISE 2 ************")
v = 1:4
v1 = v([1 2])
v2 = v(3:4)
A = [v1; v2]
A = [A, zeros(2, 2); zeros(2,2), eye(2)]
A(A == 0) = -1
A([2, 3], :) = []
A(:, [2, 3]) = []
f = @(x) sqrt(1 + x.^2);
g = @(x) log(2 + cos(x));
I = [-6, 6];
figure
hold
fplot(f, I, 'c')
fplot(g, I, 'm')
grid
xlabel('x')
ylabel('y')
B = f(A)
C = g(A)
B' - C'

%% EXERCISE 3
disp("************ EXERCISE 3 ************")
f = @(x, y) (x - y)./(x + y);
I = [-1 1 -1 1];
figure
fsurf(f, I)
xlabel('x')
ylabel('y')
zlabel('z')
figure
fcontour(f, I)
xlabel('x')
ylabel('y')
grid
figure
subplot(2, 1, 1)
fsurf(f, I)
xlabel('x')
ylabel('y')
zlabel('z')
subplot(2, 1, 2)
fcontour(f, I)
xlabel('x')
ylabel('y')
grid