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Data Analysis using Statistics Software Such as SPSS, Minitab, MS-Excel, STATA, Eviews, etc. Stat-Soft

Using Mathematica Built-in Functions (2014)

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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.

Mathematica Built-in Functions

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.

Introduction to Mathematica

R Programming Language

MCQs General Knowledge

Introduction to Mathematica (2013)

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MATHEMATICA created by Steven Wolfram, a product of Wolfram Research, Inc. Mathematica is available for different operating systems, such as SGI, Sun, NeXT, Mac, DOS, and Windows. This introduction to Mathematica will help you to understand its use as a mathematical and programming language with numerical, symbolic, and graphical calculations.

Introduction to Mathematica

  1. A calculator for arithmetic, symbolic, and algebraic calculations
  2. A language for developing transformation rules, so that general mathematical relationships can be expressed
  3. An interactive environment for the exploration of numerical, symbolic, and graphical calculations
  4. A tool for preparing input to other programs, or to process output from other programs

Getting Started with Mathematica

Starting Mathematica will open a fresh window or a notebook, where we do all mathematical calculations and some graphics. Initially window’s title is “untitled-1” which can be changed after saving the notebook by name as desired. Mathematica notebook with text, graphics, and Mathematica input and output

Introduction to mathematica notebook

Entering Expressions

Type 1+1 in the notebook and press the ENTER key from the keyboard. You will get an answer in the next line of work area. This is called evaluating or entering the expression. Note that Mathematica places “In[1]:=” and “out[1]=” (without quotation marks) labels to 1+1 and 2 respectively. You will also see a set of brackets on the right side of the input and output. The innermost brackets enclose the input and output while the outer bracket (larger bracket) groups the input and output. Each bracket contains a cell. Each time you enter or change the input you will notice that the “In” and “Out” labels will also be changed.

Basic Arithmetic

Mathematica can perform basic operations of additions (+), subtraction (-), multiplication (*), division (/), exponentiation(^), etc. For example, write the following line for basic arithmetic in Mathematica

2*3+4^2
5*6
2(3+4)
(2-3+1)(1+2/3)-5^(-1)
6!

Using Previous Results in Mathematica

Often we need the output of the first (previous) calculations in our next (coming) computation. For this purpose % symbol can be used to refer to the output of the previous cell. For example,

2^5
% + 100

Here 2^5 is added in 100.

%% refers to the result before the last results (2nd last).

Exact vs Approximation

Mathematica can give approximate results; when we need

3^20/2^21 produces $\frac{3486784401}{2097152}$

We can force Mathematica to approximate results in decimals by putting decimals in expressions (with any digit or number) such as

3.0^20/ 2^21

For a decimal in number in an expression, Mathematica considers it to be an approximation rather than an exact number.

Wolfram Mathematica

R Frequently Asked Questions

Matlab as a Calculator

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MATLAB stands for “Matrix Laboratory” and is an interactive, matrix-based system and fourth-generation programming language from Mathworks Inc., which is mathematics software. Matlab helps to perform statistical analysis and gives the user complete freedom to implement specific algorithms and perform complex custom-tailored operations.

Matlab has a command-driven approach. Commands with appropriate arguments are written after the Matlab command prompt >>. The Matlab program provides the user with a convenient environment for performing many types of calculations. This introduction to Matlab will help users understand its importance and variety of applications in different scientific fields.

Matlab as a Calculator

Matlab has three primary windows.

1) Command windows
2) Graphics Windows
3) Edit Windows used to write M-Files

The common way to operate Matlab is to enter commands in the command window.

Matlab as a Calculator

>> 55 – 16
ans = 39
>> ans + 11
ans =50

Matlab assigns the results ans whenever you do not explicitly assign the calculations to a chosen variable.

>> a = 4                   % assigns a scalar quantity to a
>> a                         % Prints the scalar quantity in command windows
>> a = 4                   % suppressed echo printing
>> a =4; A=6; x=1;  % multiple variable definition

Note: Matlab treats names as Case-Sensitive.

>> format long
>> pi
>> format short
>> pi
Matlab as Calculator

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