EDU>> f=inline('exp(-x.^2.5)')
f =
     Inline function:
     f(x) = exp(-x.^2.5)
EDU>> n=100; h=1/n; x=0:h:1; c=[1 repmat([4 2],1,49) 4 1]; (h/3)*c*f(x)'
ans =
      0.78126
EDU>> format long
EDU>> n=100; h=1/n; x=0:h:1; c=[1 repmat([4 2],1,49) 4 1]; (h/3)*c*f(x)'
ans =
   0.78125895570302
EDU>> n=10000; h=1/n; x=0:h:1; c=[1 repmat([4 2],1,49) 4 1]; (h/3)*c*f(x)'
??? Error using ==> *
Inner matrix dimensions must agree.

EDU>> n=10000; h=1/n; x=0:h:1; c=[1 repmat([4 2],1,n/2-1) 4 1]; (h/3)*c*f(x)'
ans =
   0.78125895340946
EDU>> help quad

 ...

EDU>> f
f =
     Inline function:
     f(x) = exp(-x.^2.5)
EDU>> quad(f,0,1)
ans =
   0.78125900309009
EDU>> ans - 0.78125895340946
ans =
    4.968063016530522e-008
EDU>> quad(f,0,1,1e-11)
ans =
   0.78125895341267
EDU>> quad(f,0,1,1e-13)
ans =
   0.78125895340949
EDU>> quad(f,0,1,1e-14)
ans =
   0.78125895340946
EDU>> quad(f,0,1,1e-15)
ans =
   0.78125895340946
EDU>> quadl(f,0,1,1e-15)
ans =
   0.78125895340946
EDU>> help quadl

...

EDU>> x=linspace(-pi,pi,1000);
EDU>> N=50; 
EDU>> y=zeros(size(x)); for k=1:N, y=y+((4/pi)/(2*k-1))*sin((2*k-1)*x); end
EDU>> plot(x,y)
EDU>> grid on
EDU>> N=500;
EDU>> y=zeros(size(x)); for k=1:N, y=y+((4/pi)/(2*k-1))*sin((2*k-1)*x); end
EDU>> plot(x,y)
EDU>> x=linspace(-pi,pi,100000);
EDU>> y=zeros(size(x)); for k=1:N, y=y+((4/pi)/(2*k-1))*sin((2*k-1)*x); end

EDU>> x=linspace(-pi,pi,10000);
EDU>> y=zeros(size(x)); for k=1:N, y=y+((4/pi)/(2*k-1))*sin((2*k-1)*x); end
EDU>> plot(x,y)
EDU>> y=0; for k=1:N, y=y+((4/pi)/(2*k-1))*sin((2*k-1)*x); end
EDU>> size(y)
ans =
           1       10000

EDU>> help ode45

 ...

EDU>> f=inline('[y(2); y(3); -y(1)-y(2)-y(3)]','x','y')
f =
     Inline function:
     f(x,y) = [y(2); y(3); -y(1)-y(2)-y(3)]
EDU>> [x,y]=ode45(f,[1 10],[0 1 2]');
EDU>> size(x)
ans =
    69     1
EDU>> size(y)
ans =
    69     3
EDU>> plot(x,y)
EDU>> legend('y','v','w')
EDU>>