Symbolic Math Toolbox

Creating Symbolic Math Functions

There are two ways to create functions:

• Use symbolic expressions
• Create an M-file

Using Symbolic Expressions

The sequence of commands

• syms x y z
  r = sqrt(x^2 + y^2 + z^2)
  t = atan(y/x)
  f = sin(x*y)/(x*y)
  

generates the symbolic expressions r, t, and f. You can use diff, int, subs, and other Symbolic Math Toolbox functions to manipulate such expressions.

Creating an M-File

M-files permit a more general use of functions. Suppose, for example, you want to create the sinc function sin(x)/x. To do this, create an M-file in the @sym directory:

• function z = sinc(x)
  %SINC The symbolic sinc function
  %     sin(x)/x. This function
  %     accepts a sym as the input argument.
  if isequal(x,sym(0))
     z = 1;
  else
     z = sin(x)/x;
  end
  

You can extend such examples to functions of several variables. See the MATLAB topic Programming and Data Types for a more detailed discussion on object-oriented programming.

Symbolic and Numeric Conversions

Using the Symbolic Math Toolbox