## Free-form inputs

### To compute, press `SHIFT + ENTER`

`In[1]:= 3 + 9`

`SHIFT + ENTER`

`Out[1]:= 12`

### To suppress output, add `;`

after the line

`In[1]:= 3 + 9;`

`SHIFT + ENTER`

-> no output

### You can execute multiple lines at once

`In[1]:= a = 2`

`b = a + 2`

`c = b ^ 3`

`SHIFT + ENTER`

`Out[1]:= 2`

`Out[2]:= 4`

`Out[3]:= 64`

Starting from now, when we have output, it means that in the end of the previous line, we press `SHIFT + ENTER`

.

### To get the most recent output, use `%`

`In[1]:= 3 + 9`

`Out[1]:= 12`

`In[1]:= % + 5`

`Out[1]:= 17`

## Basics in Programming

### Variable

A variable starts with letters. If you want, you may add numbers into the variable name. It is much better if you start the variable name with lowercase

`In[1]:= myVariable123 = 2`

`Out[1]:= 2`

Please notice how I join the two words and the number into a single word. If you put space between the variable name, it will indicate multiplication

`In[1]:= x = 3;`

`5 x x`

`Out[1]:= 45`

To clear the variable, use `Clear`

function

`In[1]:= x = 2`

`Out[1]:= 2`

`In[2]:= 2 x`

`Out[2]:= 4`

`In[3]:= Clear[x]`

`In[4]:= 5 x x`

`Out[4]:=`

\(5x^2\)

### Conditional Statement

The `if`

contains three parts i.e. test, then (what to do if true), and else (what to do if false). The syntax is as follows

`If[test, then, else]`

Examples

`In[1]:= If[5<8, Print["5 is less than 8"], Print["5 is more than 8"]`

`5 is less than 8`

### List

List of items are indicated by `{ ... }`

`In[1]:= {1, 2, 3} * 2`

`Out[1]:= {2, 4, 6}`

The index of the list starts from 1

`In[1]:= {3, 8, 2, 9}[[3]]`

`Out[1]:=2`

### Loop

The syntax used for the loop in Mathematica is as follows

`For[start, test, incr, body]`

`start`

indicate the condition when the loop is started (initialization)

`test`

indicate the condition to check during the loop

`incr`

indicate the increment happen on each loop

`body`

indicate the operation done during the loop

Example:

`In[1]:= For[i=0, i<4, i++, Print[i]]`

`0`

`1`

`2`

`3`

If you want to add more command on each section, separate the command using semicolon `;`

Example

`In[1]:= For[i = 0, i < 4, i++, Print[i]; Print["hello"]]`

`0`

`hello`

`1`

`hello`

`2`

`hello`

`3`

`hello`

## Data Visualisation

### Plot

You can plot single function using the following command

`Plot[f, {x ,`

\(x_{min}\) `,`

\(x_{max}\) `}]`

Example

`In[1]:=Plot[Sin[x], {x, 0, 6 Pi}]`

If you want to plot more than one functions, use list in the functions

`Plot[{f1, f2, ... fn}, {x ,`

\(x_{min}\) `,`

\(x_{max}\) `}]`

Example

`Plot[{Sin[x], Cos[x]}, {x, 0, 6 Pi}]`

### ListPlot

ListPlot function can be used to plot points. The syntax is as follows

`ListPlot[{y1, y2, ... yn}]`

Example

`ListPlot[{1, 3, 5}]`

### ListLinePlot

ListLinePlot can be used to plot a line through the points. The syntax is as follows

`ListLinePlot[{y1, y2, ... yn}]`

Example

`ListLinePlot[{1, 3, 5, 8}]`

### Manipulate Commands

Manipulate is used to see the changes in the output when the input is changed

Example

`Manipulate[Plot[Sin[a x], {x, 0, 6}], {a, Pi, 3 Pi}]`

## Comments