% 1a.















% 1b.

[r, th] = meshgrid(0:.1:2, 0:pi/20:2*pi);
x1=r.*cos(th);
y1=r.*sin(th);
z1=r;
surf(x1,y1,z1), hold on

[t, ph] = meshgrid(0:pi/20:2*pi, 0:pi/20:pi/4);
x2 = sqrt(8)*sin(ph).*cos(t);
y2 = sqrt(8)*sin(ph).*sin(t);
z2 = sqrt(8)*cos(ph);
surf (x2,y2,z2)





% 2a.

syms n;
digits(4)
vpa(symsum(((-1)^n)/n^2, 1, 100))



% 2b.

syms m;
symsum(1/(m^2), 1, inf)


% 3

syms x y, f = (y*atan(x*y))/(1+x^2*y^2)
fx = diff(f,x)
diff(fx,y)

% 4, I let x and y be a and b respectively.

syms a b, g = (a*2+ b*3)*exp(a + b)

ig = int(g,b,0,1-a)
iga = int(ig,-1,1)