function [M,K,F] = calc_discr_Galerkin_1D(N,dx,k,u,f)

M = sparse(N,N);
K = sparse(N,N);
F = zeros(N,1);
%
for i=1:N
  if i==1  
    M(i,i) = dx(i+1-1)/3;
    M(i,i+1) = dx(i+1-1)/6;
  elseif i<N   M(i,i-1) = dx(i-1)/6;
    M(i,i) = dx(i-1)/3 + dx(i+1-1)/3;
    M(i,i+1) = dx(i+1-1)/6;
  else
    M(i,i-1) = dx(i-1)/6;
    M(i,i) = dx(i-1)/3;
  end;
end;
%
for i=1:N
  if i==1  K(i,i) = k/dx(i+1-1) - u/2;
    K(i,i+1) = -k/dx(i+1-1) + u/2;
  elseif i<N   K(i,i-1) = -k/dx(i-1) - u/2;
    K(i,i) = k/dx(i-1) + u/2 + k/dx(i+1-1) - u/2;
    K(i,i+1) = -k/dx(i+1-1) + u/2;
  else  K(i,i-1) = -k/dx(i-1) - u/2;
    K(i,i) = k/dx(i-1) + u/2;
  end;
end;
%
for i=1:N
  if     i==1  F(i) = f(1)*dx(2-1)/3 + f(2)*dx(2-1)/6;
  elseif i<N   F(i) = f(i-1)*dx(i-1)/6 + f(i)*(dx(i-1)+dx(i+1-1))/3 + f(i+1)*dx(i+1-1)/6;
  else         F(i) = f(N-1)*dx(N-1)/6 + f(N)*dx(N-1)/3;
  end;
end;