Introduction to Matlab

14  Command Summary

The following Matlab examples illustrate some commonly used Matlab syntax. Consult this list if you need to know small details (where punctuation occurs for example).

 x  =  ( 22/7 -16 + 1.9 )*3^2 ;
 y  =  exp( -pi*i ) ;
 
 ezplot('x^2/(1+x^2)')
 ezplot('x^2+y^2-4',[0,2],[0,2])
 ezplot( 'cos(t)','sin(t)',[0,2*pi])
 fplot( '[ sin(x), x-x^3 ]',[0,pi] )
 
 ezsurf( 'xy^2 / ( x^2+y^4 )' )
 ezsurf('sqrt(1-t^2)*cos(s*pi)', ...
          'sqrt(1-t^2)*sin(s*pi)', 't', [-1,1] )
 
 x =  0:.05:1 ;       
 fx =  ( 1 + x ) .* cos( x ) ./ ( 3 - x.^2 )   ;
 plot(  x,fx,'--' ) ;
 
 x = -2:.2:2  ;  y = 0:.2:2 ;     
 [X , Y] =  meshgrid( x,y ) ;      
 Z  =  X .* Y .* exp( -( X.^2 + Y.^2 ) ) ;
 surf(X,Y,Z)
 
 A  =  [  2 3 4; 5 6 7; -1 -1 1] ;
 col1 = A(:,1) ; row2 = A(2,:) ;
 A_lower = A(2:3,2:3) ;
 odd  =  1:2:9 ; odd = odd' ;
 
 b  =  [ 1;2;3 ] ;  x = A \ b ;     %  Solve A x = b
 [ U,Lam ] = eig(A) ;               %  Find eigenvalues
                                    %    & eigenvectors.
 
 I   = eye( 3 ) ;              % Set up special matrices
 S  =  rand(4,1) ;
 T  = diag( ones(4,1),-1 ) ...
        + diag( -2*ones(5,1) ) ...
          + diag( ones(4,1),1 );
 
 x = 3 ;
 for  k = 1:30
      x_new  = ( x + 3/x )/2 ;
   if abs( x - x_new ) < 1.e-12 , break , end
      x = x_new ;
 end
 
 function   yp  =  ff( t,y )           % A new function.
 yp =   y / ( 1+ t^2 ) ;