%
% - File name : nonlin_onevar_1.m (Generated by Hee Jung : fall/1999)
% - Solve nonlinear equations of one variable 
% - Example problem : solve  
%
%                            0.1*e^(x) + sin(x) -5 = x
%
%                     for x.
% - Method 1 : Express equations in homogeneous form (i.e. f(x)=0) and plot 
%              x versus f(x) to see which values of x approximately satisfy the equations
%              and zoom in the plot to find x more accurately. This method can not give 
%              exact solutions, but provides a rough idea what the solution is. 
%
clear   % removes all variables from the workspace

% Define x variables
x = 0:0.01:5;   % 501 numbers betweeon  zero and five.

% Define function  f(x) as a list of numbers corresponding to x
f = 0.1*exp(x) + sin(x) - 5 - x;

% Draw the figure(1) : x versus f(x)
figure(1)
clf
plot(x,f)
xlabel('x'); ylabel('f(x) = 0.1*e^x + sin(x) - 5 - x');
title('(x) v.s. f(x) = 0.1*e^x + sin(x) - 5 - x');
grid on

% Zoom in the area where f(x) is close to zero, which is about at x=4.65
figure(2)
clf
plot(x,f)
axis([4.6,4.7, -1, 1])   % set the x axis interval
xlabel('x'); ylabel('f(x) = 0.1*e^x + sin(x) - 5 - x');
title('(x) v.s. f(x) : Zoom in ');
grid on

% From  figure(2), the solution of this problem can be found as about x=4.670 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Note : To apply this method, you may need some trial & error.
%        If there's no solution in the x interval you specified, 
%        you need to  try a different interval. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

