clc
clear all
close all

%% EXERCISE 1
R1 = 1000;
R2 = 200;
ii = 10/100;
w_R1_0 = R1*(1 + ii)^-3*(1 - (1 + ii)^-4)/ii;
auxString = sprintf("w(R1, 0) = %.3f", w_R1_0);
disp(auxString)
w_R2_0 = R2*((1 + ii)^-9)/ii;
auxString = sprintf("w(R2, 0) = %.3f", w_R2_0);
disp(auxString)
w_0 = w_R1_0 + w_R2_0;
auxString = sprintf("w(0) = %.3f", w_0);
disp(auxString)
w_7 = w_0*(1 + ii)^7;
auxString = sprintf("w(7) = %.3f", w_7);
disp(auxString)

%% EXERCISE 2
f = @(x, y) sqrt(y - x.^2);
I = [-4 4 0 4];
fsurf(f, I);
xlabel('x')
ylabel('y')
zlabel('z')

%% EXERCISE 3
A = [2 1 0; 0 1 -1; 0 2 4];
[Q, L] = eig(A)
v_normalized = [1/sqrt(6), ...
    1/sqrt(6), -2/sqrt(6)]

%% EXERCISE 4

% Copy the matrix A in matrix B
B = A;

% Set the element in position (1, 3) equal to 2
B(1, 3) = 2

% Set all the elements of the third row equal to 3
B(3, :) = 3

% Delete the second row and the second column
B(2, :) = [];
B(:, 2) = []

% Functions
g = @(x) x.^2 - 2*x + cos(x);
h = @(x) 10*sqrt(1 + sin(x));
figure
hold on
grid on
I = [-6 6];
fplot(g, I)
fplot(h, I)
xlabel('x')
ylabel('y')
C = g(B) + h(B)'