Evaluate Symbolic Expression in MATLAB Programming

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Matlab allows user to create symbolic math expressions. This is useful when user don't want to immediately compute an answer, or when user have a math "formula" to work on but don't know how to "process" it.

Matlab allows symbolic operations several areas including:

  • • Calculus

  • • Linear Algebra

  • • Algebraic and Differential Equations

  • • Transforms (Fourier, Laplace, etc)

These key function in Matlab is used to create a symbolic representation of data is: sym() or syms if user have multiple symbols to make.

Defining Symbolic Expressions

User can define symbolic functions using the sym function command and syms function command. Here is an example for creating a symbolic function for (a*X^2) + (b*x) + c:

>> syms a b c x % define the symbolic math variables

>> f = sym('a*x^2 + b*x + c');

Evaluation of Symbolic Expressions

The keyfunction subs (which stands for substitute) is for replacing symbolic variables with either new symbolic variables or with acutal values. The syntax of the subs function is: subs( symbolic_function, list_of_symbols, list_of_values). Here is an example:

>> f = sym('a*x^2 + b*x + c');

>> subs(f,x,5)

ans =

25 * a + 5 * b + c

>> subs(f,[x a b c],[5 1 2 3])

ans =


Plotting Symbolic Function

In Matlab, user can plot a symbolic function over one variable by using the function ezplot function. Here is an example:

>> y = sin(x)

y =


>> ezplot(y)