%
% Matrix-vector product for problem 6
%
function ax=mvp5(x)
ax=d2(x)+d1(x)+x;

%
% discrete first derivative
%
function y1=d1(x);
n=length(x);
h=1/(n+1);
%
% Make sure it's a column vector
%
y1=zeros(n,1);
y1(1)=x(2);
y1(n)=-x(n-1);
for i=2:n-1
    y1(i)=x(i+1)-x(i-1);
end
y1=.5*y1/h;


%
% discrete second derivative
%
function y2=d2(x);
n=length(x);
%
% Make sure it's a column vector
%
y2=zeros(n,1);
h=1/(n+1);
y2(1)= -x(2)+2*x(1);
y2(n)=  -x(n-1) + 2*x(n);
for i=2:n-1
    y2(i) = - x(i-1) + 2*x(i) - x(i+1);
end
y2=y2/(h*h);