**Task:** get basic knowledge of how to work with Symbolic Toolbox in the MATLAB software package (Part 2).

Operations on Symbolic Expressions

Once an expression or variable is declared as a symbolic object, we can perform standard mathematical operations such as given in the table below.

Function Description |
Function Description |

horner(S) | transforms S into the Horner nested polynomial format |

[N,D] = numden(S) | returns two symbolic numerator and denominator expressions |

sym(S,’?’); where ? may be f,r,e, or d | symbolic to numeric conversion: f is floating point, r = rational form, e = rational plus an error term, d = decimal expansion when followed by digits(N) |

poly2sym(c) | converts the polynomial vector c into a symbolic polynomial |

pretty(S) | produces a typeset type display |

A+B | symbolic addition of A+B |

A/B | symbolic division of A/B |

A*B | symbolic multiplication of AB |

S^p | symbolic power S^p |

A-B | symbolic subtraction A-B |

Example:

syms y

p1 = 1/(y-3);

p2 = 3*y/(y+2);

p3 = (y+4) *(y-3) *y;

% Now operate:

**Solutions to Equations**

To solve a single equation, we use:

That is, find what value of the independent variable makes ; var is optional.

– If more than one variable is present, the variable to solve for set with var is:

% Contains four variables

% Solve for

%quadratic equation

To solve a system of equations, use:

The var_{1}, …,var_{n}are the variables to solve for. They must be declared as symbolics using syms.

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