%% Homework 1
%
% Section 1.2: 2c, 3d, 12
%
% Show that the nesting algorithm for computing $\displaystyle f(x) = x^2 + 3x + 2$
% reduces roundoff error in 3-digit machine arithmetic.
%
% Section 2.1: 3a, 5b, 11c, 14

%% Computer Assignment 1
%
% Complete the following assignment and turn it in to the eee.uci.edu
% DropBox by 11:59pm, Thursday, 9/30.  You should use MATLAB's publish
% functionality and submit both a .pdf file and your original m-file. If
% you have any questions about this, please ask.  You should just modify
% this file when you submit.
%
% Implement the bisection method (Algorithm 2.1 on pg. 49) and use it to
% compute the root of 
%
% $$6(e^x - x) = 7 + 3 x^2 + 2 x^3$$
%
% that lies in the
% interval $[-1,1]$.
%
%  INPUT endpoints a,b; tolerance TOL; maximum number of iterations Nmax
%  OUTPUT approximate solution x of f(x) = 0; or failure message
%
%  Step 1: Set i = 1;
%        A = f(a);
%  Step 2:  While i <= Nmax do 3-6:
%       Step 3: Set p = (a+b)/2; P = f(p);
%       Step 4: If P = 0 or (b-a)/2 < TOL then
%       Step 5: OUTPUT(p);
%               STOP.
%       Step 6: If A*P > 0 then set a = p; A = P;
%                   Else set b = p;
%  Step 7: OUPUT('Method failed after Nmax iterations, Nmax = ', Nmax);
%          STOP.

%% Solution
%
% Put your name and solution here.