%Problem 1
A = zeros(5);
for p=1:5
    for q=1:5
        A(p,q) = (p*q^2*sin(3*p+q))/(3+p+3*q);
    end
end

%1.1
b = [1; 1; 1; 1; 1];
x = A\b;
J1 = x(3);
J1

%1.2
B = A^2 + pi*A;
v = eig(3);
J2 = sum(abs(v));
J2

%Problem 2
syms x
f = (x.^2+2*x-3)./(2+sin(x));
d = diff(f,5);
g = subs(d, x, 3);
J3 = double(g);
J3

%Problem 3
J4=integral(@(x)(x.^2+2*x-1)./(2+sin(x)), -1, pi)

%Problem 4
g = @(x, y)(sin(x.*y/3).^3).*x.^2.*y
J5 = integral2(g, 0, pi/2, 1, 3)

%Problem 5
syms t;
y = dsolve('D2y-4*Dy+3*y=cos(3*t/4)', 'y(0) = 0', 'Dy(1) = 0');
s=subs(y, t, 3/10);
J6=double(s);
J6

%Problem 6
ezplot('(sin(x)+3*cos(x)/5)/(3/15+x)', [0,2*pi])
[x,y]=fminbnd(@(x)(sin(x)+3*cos(x)/5)/(3/15+x), 3, 5);
J7 = y

%Problem 7
ezsurf('x*exp(-x^2 - (y^4)/4)')
[x, y] = fminsearch('x(1)*exp(-x(1)^2 - (x(2)^4)/3)', [-0.5, 0.5]);
J8 = y

%Problem 8
C = [ones(1,10), -sin(3)];
z=roots(C)
J9 = sum(z.^3)