% Small root finding example.
% Ken Jackson    6 Sept. 2007

% First plot the function exp(x) - sin(x)

 x = -3*pi : .001 : pi/2;

 plot(x,exp(x)-sin(x),'-b')

 hold on
 plot([-3*pi, pi/2], [0,0], '-k') 
 plot([0,0], [-1,exp(pi/2)], '-k')
 title('Graph of exp(x) - sin(x)')
 hold off


% Now use Newton's method to find the root closest to zero

  format long e

  r = -3
  f = exp(r) - sin(r)
  fp = exp(r) - cos(r)

  while  abs(f) > 1.e-12 ,
     r = r - f / fp
     f = exp(r) - sin(r)
     fp = exp(r) - cos(r)
  end