# Symbolic Math in Matlab

Matlab allows you to create symbolic math expressions. This is useful when you don't want to immediately compute an answer, or when you 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)

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

Below is an example of creating some symbolic fractions and square roots:

## Defining Symbolic Expressions

We can define symbolic functions using the sym command and syms command. Here is an example of creating a symbolic function

for (a*X^2) + (b*x) + c:

From now on we can use the f symbol to represent the given function.

## Evaluation of Symbolic Expressions

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

## Plotting Symbolic Function

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

If you want to see something cool, try:

Or plotting a polynomial equation:

## Integration and Derivation

Matlab can also compute many integrals and derivatives that you might find in Calculus or many advanced engineering courses.

Source: www.cs.utah.eduCategory: Bank

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