function amath3132hw1
% Instructor's solution for amath 3132 hw 1
  disp('----------My Information-------------')
  
  Name = 'Jahrul';
  Surname = 'Alam';
  ID = 123456789;
  
  fprintf('  Professor:  %s %s (ID: %d) \n', Name, Surname, ID);
  
  
  disp('  ------------------------------------------------  ')  
  disp('  ')
  
  disp('Hit enter to proceed')
  pause
  clear all; close all;
  
  disp('  ----------   Solution to Question #1  ----------  ')  
  disp('  ')
  disp('Q.1(a)')
  disp('The algorithm is available in the lecture note')
  disp('  ')

  fprintf('Q.1(b): convert to binary using conver_decimal\n')
  
  fprintf('Q.1(c):\n')
  res=convert_decimal(6789);
  fprintf('6789 to binary %s\n',res)

  fprintf('Q.1(d):\n')
  res=convert_decimal(191);
  fprintf('191 to binary %s\n',res)

  res=convert_decimal(396);
  fprintf('396 to binary %s\n',res)

  res=convert_decimal(3196);
  fprintf('3196 to binary %s\n',res)
  
  res=convert_decimal(9164);
  fprintf('9164 to binary %s\n',res)

  disp('  ')
  disp('  ------------------------------------------------  ')  
  disp('  ')
  
  disp('Hit enter to proceed to next question')
  pause
  
  disp('  ----------   Solution to Question #2  ----------  ')  
  disp('  ')

  fprintf('2(b): truncation error for x=0.5\n')
  x=0.5;
  fprintf('n=1, truncation error=%d\n',lon(x,1))
  fprintf('n=2, truncation error=%d\n',lon(x,2))
  fprintf('n=3, truncation error=%d\n',lon(x,3))
  fprintf('n=4, truncation error=%d\n',lon(x,4))

  disp(' ')  
  fprintf('2(c): relative truncation error for x=0.5\n')
  x=0.5;
  fprintf('n=1, rel. truncation error=%d\n',lon(x,1)/log(1.0+x))
  fprintf('digits=%d\n',floor(-log10(lon(x,1)/log(1.0+x)/0.5)))
  
  fprintf('n=2, rel. truncation error=%d\n',lon(x,2)/log(1.0+x))
  fprintf('digits=%d\n',floor(-log10(lon(x,2)/log(1.0+x)/0.5)))

  
  fprintf('n=3, rel. truncation error=%d\n',lon(x,3)/log(1.0+x))
  fprintf('digits=%d\n',floor(-log10(lon(x,3)/log(1.0+x)/0.5)))

  
  fprintf('n=4, rel. truncation error=%d\n',lon(x,4)/log(1.0+x))
  fprintf('digits=%d\n',floor(-log10(lon(x,4)/log(1.0+x)/0.5)))

  fprintf('2(d): plot relative truncation error\n')
  
  x=linspace(0,1,32);
  err(1:length(x),1:4)=0;
  for i=1:length(x)
    err(i,1)=lon(x(i),1)/log(1.0+x(i));
    err(i,2)=lon(x(i),2)/log(1.0+x(i));
    err(i,3)=lon(x(i),3)/log(1.0+x(i));
    err(i,4)=lon(x(i),4)/log(1.0+x(i));
  end
  
  plot(x,err(:,1),'o-',x,err(:,2),'x-',x,err(:,3),'s-',x,err(:,4),'*')
  set(gca,'fontsize',18)
  xlabel('x');ylabel('error');
  legend('n=1','n=2','n=3','n=4',2)

  disp('  ')
  disp('Hit enter to proceed to next question')
  pause
  
  disp('  ----------   Solution to Question #3  ----------  ')  
  disp('  ')

  t=linspace(0,2*pi);
  % x versus t  
  x=3*cos(2*t);
  plot_xy(t,x,1,'o-')
  xlabel('t');ylabel('x')
  disp('Hit enter to proceed to next plot')
  pause

  % y versus t  
  y=5*sin(3*t);
  plot_xy(t,y,2,'x--')
  xlabel('t');ylabel('y')
  disp('Hit enter to proceed to next plot')
  pause

  % x versus y
  plot_xy(x,y,3,'d:')
  xlabel('x');ylabel('y')
  disp('Hit enter to proceed to next plot')
  pause
  xbound=[-3 3];
  ybound=[-3,3];
  plot_surf(xbound,ybound)
  disp('Hit enter to proceed to finish')
  pause

  
function result=convert_decimal(n)	
%this function converts a given decimal number n to a binary
%number.
%Version 1.0
%The following algorithm uses less knowledge of matlab, and hence
%requires more programming work.
  res(1:128)=0;
  i=1;
  p=n;
  res(i)=mod(p,2);
  while(p >0)
    i=i+1;
    if(mod(p,2)==1)
      p=(p-1)/2;
    else
      p=p/2;
    end
    res(i)=mod(p,2);
  end	
  res=res(1:i-1);
  res=fliplr(res);
  result='000000000000000000000000000000000';
  for(i=1:length(res))
    result(i)=num2str(res(i));
  end
  result=result(1:length(res));
  
  
  
  
function result=lon(x,n)
  
  sum=0;
  for i=1:n
    sum = sum + (x^i/i * (-1)^(i+1));
  end
  
  
  err=(log(1.0+x)-sum);%/log(1.0+x);

  result=abs(err);
  
  
function plot_xy(x,y,fign, opt)
  if(nargin<4) 
    opt='o-';
  end
  figure(fign);clf
  plot(x,y,opt)
  set(gca,'fontsize',18);
  grid on;
  axis tight;
  
function plot_surf(xbound,ybound)
  x=linspace(xbound(1),xbound(2));
  y=linspace(ybound(1),ybound(2));
  [x,y]=meshgrid(x,y);
  
  z=(x.^2-y.^2).*exp(-x.^2-y.^2);
  surf(x,y,z)
  set(gca,'fontsize',16)
  shading interp;
  title('Example for surface plot')
  xlabel('x')
  ylabel('y')
  zlabel('z')