# Using Mathematica Built-in Functions (2014)

### Introduction to Mathematica Built-in Functions

There are thousands of thousands of Mathematica Built-in Functions. Knowing a few dozen of the more important will help to do lots of neat calculations. Memorizing the names of most of the functions is not too hard as approximately all of the built-in functions in Mathematica follow naming convention (i.e. names of functions are related to the objective of their functionality), for example, the Abs function is for absolute value, Cos function is for Cosine and Sqrt is for the square root of a number.

The important thing than memorizing the function names is remembering the syntax needed to use built-in functions. Remembering many of the built-in Mathematica functions will not only make it easier to follow programs but also enhance your programming skills.

### Important and Widely Used Mathematica Built-in Functions

The following is a short list related to Mathematica Built-in Functions.

• Sqrt[ ]:   used to find the square root of a number
• N[ ]:   used for numerical evaluation of any mathematical expression e.g. N[Sqrt[27]]
• Log[  ]: used to find the log base 10 of a number
• Sin[  ]: used to find trigonometric function Sin
• Abs[  ]: used to find the absolute value of a number

Common Mathematica built-in functions include

1. Trigonometric functions and their inverses
2. Hyperbolic functions and their inverses
3. logarithm and exponential functions

Every built-in function in Mathematica has two very important features

• All Mathematica built-in functions begin with Capital letters, such as for square root we use Sqrt, for inverse cosine we use the ArCos built-in function.
• Square brackets are always used to surround the input or argument of a function.

For computing the absolute value -12, write on command prompt Abs[-12]  instead of for example Abs(-12) or Abs{-12} etc i.e.   Abs[-12] is a valid command for computing the absolute value of -12.

Note that:

In Mathematica single square brackets are used for input in a function, double square brackets [[ and ]] are used for lists, and parenthesis ( and ) are used to group terms in algebraic expression while curly brackets { and } are used to delimit lists. The three sets of delimiters [ ], ( ), { } are used for functions, algebraic expressions, and lists respectively.

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