function [ L, U ] = special_LU( S )
% Produces a unit lower triangular matrix L and an upper lower
% triangular U such that S = L*U.
% Note: S, L, U are all NxN matrices
S must have the following special form: it is tridiagonal
except that S(1,N) and
% Evaluate the roughly number of random points we need to get
% a relatively high level of confidence for a relative error which
% is less than 0.01 for monte carlo method in (b).
exact = 8*(pi^2)*(2-pi);
0unction in b
fun = @(x,y,z)x*sin(y)-
function [ estimate ] = starter_monte_carlo(f, x_range, y_range,
z_range, N )
% Produces a Monte Carlo approximation of the triple integral of
% over the ranges specified in x_range, y_range, and z_range, and when
% using N points.