Page 492 - Applied Numerical Methods Using MATLAB

APPENDIX G

SYMBOLIC COMPUTATION

G.1 HOW TO DECLARE SYMBOLIC VARIABLES AND HANDLE
SYMBOLIC EXPRESSIONS

To declare any variable(s) as a symbolic variable, you should use the sym or
syms command as below.

>>a = sym(’a’); t = sym(’t’); x = sym(’x’);
>>symsaxyt %or, equivalently and more efficiently

Once the variables have been declared as symbolic, they can be used in expres-
sions and as arguments to many functions without being evaluated as numeric.

>>f = x^2/(1 + tan(x)^2);
>>ezplot(f,-pi,pi)
>>simplify(cos(x)^2+sin(x)^2) %simplify an expression
ans=1
>>simplify(cos(x)^2 - sin(x)^2) %simplify an expression
ans = 2*cos(x)^2-1
>>simple(cos(x)^2 - sin(x)^2) %simple expression
ans = cos(2*x)
>>simple(cos(x) + i*sin(x)) %simple expression
ans = exp(i*x)
>>eq1 = expand((x + y)^3 - (x + y)^2) %expand
eq1 = x^3 + 3*x^2*y + 3*x*y^2 + y^3 - x^2 - 2*x*y - y^2
>>collect(eq1,y) %collect similar terms in descending order with respect to y
ans = y^3 + (3*x - 1)*y^2 + (3*x^2 - 2*x)*y + x^3 - x^2


Applied Numerical Methods Using MATLAB , by Yang, Cao, Chung, and Morris
Copyright  2005 John Wiley & Sons, Inc., ISBN 0-471-69833-4
481