symbolic1.txt

good code for matlab by mili , i than you

x = sym('x')   % defining x as a symbolic object
 
x =
 
x
 
syms y f g1 g2 g	% definition of multiple objects
whos			% types of variables in the workspace
  Name      Size         Bytes  Class

  f         1x1            126  sym object
  g         1x1            126  sym object
  g1        1x1            128  sym object
  g2        1x1            128  sym object
  x         1x1            126  sym object
  y         1x1            126  sym object

Grand total is 14 elements using 760 bytes

f= 12 + (x-1)*(x-1)*(x-2)*(x-3)  % constructing f
 
f =
 
12+(x-1)^2*(x-2)*(x-3)
 
diff(f)	% first derivative 
 
ans =
 
2*(x-1)*(x-2)*(x-3)+(x-1)^2*(x-3)+(x-1)^2*(x-2)
 
% note the chain rule for derivatives
% note the idependent variable is assumed to be x
diff(f,x,2)    % the second derivative
 
ans =
 
2*(x-2)*(x-3)+4*(x-1)*(x-3)+4*(x-1)*(x-2)+2*(x-1)^2
 
diff(f,x,3)    % the third derivative
 
ans =
 
24*x-42
 
g1= 20*x +15*y -30   % define g1
 
g1 =
 
20*x+15*y-30
 
g2 = 0.25*x + y -1;  % define g2

% g1,g2 can only have partial derivatives
% independent variables have to be identifies
diff(g1,x)
 
ans =
 
20
 
diff(g1,y)
 
ans =
 
15
 
g = [g1;g2]  % g column vector based on g1,g2
 
g =
 
[ 20*x+15*y-30]
[    1/4*x+y-1]
 
% g can be the constraint vector in optimization problems
% the partial derivatives of g with respect to design variables
% is called the Jacobian matrix
% the properties of this matrix is important for numerical techniques

xy = [x y];	% row vector of variables
J = jacobian(g,xy)  % calculating the Jacobian
 
J =
 
[  20,  15]
[ 1/4,   1]
 
ezplot(f)  % a plot of f for -2 pi < x < 2 pi

ezplot(f,[0,4])  % plot between 0 <= x <= 4
df = diff(f);
hold on
ezplot(df,[0,4])  % plotting function and derivative
% combine with MATLAB graphics - draw a line

line([0 4],[0 0],'Color','r') 
g
 
g =
 
[ 20*x+15*y-30]
[    1/4*x+y-1]
 
% to evaluate g at x = 1, y = 2.5


subs(g,{x,y},{1,2.5})

ans =

   27.5000
    1.7500