All of the mathematical operations done with MATLAB in the first 10 chapters were numerical. The operations were carried out by writing numerical expressions that could contain numbers and variables with preassigned numerical values. When a numerical expression is executed by MATLAB, the outcome is also numerical (a single number or an array with numbers). The number, or numbers, are either exact or a floating point–approximated value. For example, typing 1/4 gives 0.2500—an exact value, and typing 1/3 gives 0.3333—an approximated value.

Many applications in math, science, and engineering require symbolic operations, which are mathematical operations with expressions that contain symbolic variables (variables that don’t have specific numerical values when the operation is executed). The result of such operations is also a mathematical expression in terms of the symbolic variables. One simple example involves solving an algebraic equation that contains several variables and solving for one variable in terms of the others. If *a*, *b*, and *x* are symbolic variables, and *ax* − *b* = 0, *x* can be solved in terms of *a* and *b* to give *x* = *b*/*a*. Other examples of symbolic operations are analytical differentiation or integration of mathematical expressions. For instance, the derivative of 2*t*^{3} + 5*t* − 8 with respect to *t* is 6*t*^{2} + 5.

MATLAB has the capability of carrying out many types of symbolic operations. The numerical part of the symbolic operation is carried out by MATLAB ...

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