MATHEMATICA TUTORIAL

# Some Mathematical Functions

*Mathematica* includes a very large collection of mathematical functions. "Mathematical Functions" gives the complete list. Here are a few of the common ones.

Sqrt[x] | square root () |

Exp[x] | exponential () |

Log[x] | natural logarithm () |

Log[b,x] | logarithm to base () |

Sin[x],Cos[x],Tan[x] | trigonometric functions (with arguments in radians) |

ArcSin[x],ArcCos[x],ArcTan[x] | inverse trigonometric functions |

n! | factorial (product of integers ) |

Abs[x] | absolute value |

Round[x] | closest integer to |

Mod[n,m] | modulo (remainder on division of by ) |

RandomReal[] | pseudorandom number between 0 and 1 |

Max[x,y,...],Min[x,y,...] | maximum, minimum of , , ... |

FactorInteger[n] | prime factors of (see "Integer and Number Theoretic Functions") |

Some common mathematical functions.

• The arguments of all Mathematica functions are enclosed in square brackets. |

• The names of built-in Mathematica functions begin with capital letters. |

Two important points about functions in *Mathematica*.

It is important to remember that all function arguments in *Mathematica* are enclosed in *square brackets*, not parentheses. Parentheses in *Mathematica* are used only to indicate the grouping of terms, and never to give function arguments.

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Just as with arithmetic operations, *Mathematica* tries to give exact values for mathematical functions when you give it exact input.

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The presence of an explicit decimal point tells

*Mathematica*to give an approximate numerical result.In[4]:= |

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Since you are not asking for an approximate numerical result,

*Mathematica*leaves the number here in an exact symbolic form.In[5]:= |

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Here is the exact integer result for . Computing factorials like this can give you very large numbers. You should be able to calculate up to at least in a short time.

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Pi | |

E | (normally output as ) |

Degree | : degrees-to-radians conversion factor (normally output as ) |

I | (normally output as ) |

Infinity |

Some common mathematical constants.

Notice that the names of these built-in constants all begin with capital letters.

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This gives the exact result for . Notice that the arguments to trigonometric functions are always in radians.

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This gives the numerical value of . Multiplying by the constant Degree converts the argument to radians.

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Log[x] gives logarithms to base .

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You can get logarithms in any base b using Log[b, x]. As in standard mathematical notation, the b is optional.

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