Here are some basic Mathematica operations:

3 + 8

3 * 8

3*8 - 6

3*(8-6)

x = 3*8

x

x + 9

2x

Below each output, Mathematica offers some buttons to execute commands that it thinks you might particularly want to do on that output. For example, “Prime Factors” was one of the offerings for the “48” above. When we clicked on that button, Mathematica showed us the command that would find the prime factors of 48 and the answer it produces:

FactorInteger[48]

If you want to erase the value stored in a variable, use the “=.” operation. More interestingly, we found this by looking through the Mathematica documentation that you can access through Mathematica’s “Help” menu.

x =.

x

Some other examples of built-in operations and functions.

Integrate[ x^2, x]

Integrate[ x^2, x ]

Sqrt[ 9 ]

Sqrt[2]

N[ Sqrt[2]]

Here’s what happens if you use a palette to construct the integral from a few lines above:

∫(x^2)\[DifferentialD]x

The ContourPlot3D command plots surfaces defined by implicit equations.

ContourPlot3D[ x^2+y^2+z^2 == 4, {x,-3,3},{y,-3,3},{z,-3,3}]

Small changes to the equation we used produce all kinds of other interesting surfaces:

ContourPlot3D[ 3x^2-y^2+z^2 == 4, {x,-3,3},{y,-3,3},{z,-3,3}]

ContourPlot3D[ x^7+y^7+z^7 == 10, {x,-3,3},{y,-3,3},{z,-3,3}]

ContourPlot3D[ (x^2 + 6) -y^2+z^2 == 14, {x,-4,4},{y,-8,8},{z,-6,6}]

ContourPlot3D[ x^2+y^2-z^9 == 4, {x,-3,3},{y,-3,3},{z,-3,3}]