MATLAB Tutor, Part 7

MATLAB Tutor

Part 7: Symbolic Mathematics

If you are using the Student Version of MATLAB, then you have access to the optional Symbolic Math Toolbox. If you are using a professional (non-student) version, then you must purchase this toolbox separately. If you do not know whether your version of MATLAB is equipped with the toolbox or not, try a few of the following exercises. If they work, you’ve got it. If not, you will have to skip over any exercise that asks you to perform computations with variables that have not been assigned numeric values and should be treated as symbols.

MATLAB’s Symbolic Math Toolbox uses Maple, a powerful computer algebra system, to manipulate and solve symbolic expressions.

Whenever you want to use symbolic mathematics, you must use the syms operator to alert MATLAB that you are using a symbolic variable, and that it does not have a specific value. Enter

     syms x   % x is a symbolic variable
     f = 3*x^2 - 5*x + 1   % sym expression
     g = x^2 + 2*x   % so is g
     f + g

Compare the result of step 1 to the one you get when you enter the following statements:

x = 5 % x has a numeric value
f = 3*x^2 - 5*x + 1

MATLAB has a plot command called ezplot that will plot symbolic functions. Enter

     syms x
     f = 3*x^2 - 5*x + 1
     ezplot(f, [- 3,2])

To substitute a number or a symbol into a symbolic expression, use the subs command. Enter

     subs(f, x, - 2)
     syms q
     subs(f, x, q)

Below we declare four symbolic variables at once using the syms command and solve a quadratic equation using the solve command. Enter

     syms a b c t   % Create symbolics
     g = a*t^2 + b*t + c
     solve(g, t)   % Solve g = 0 for t