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Wolfram Language Fast Introduction for Math Students
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Interactive Models

The Manipulate command lets you interactively explore what happens when you vary parameters in real time:

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⨯ 
Manipulate[Plot[Sin[f x], {x, -3, 3}, Filling -> Axis], {f, 1, 5}]
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A single Manipulate command can have multiple controllers, and the Wolfram Language automatically chooses the best layout of those controllers for you:

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Click for copyable input
⨯ 
Manipulate[Plot[Sin[f*x + p], {x, -3, 3},
  Filling -> fill,
  PlotStyle -> color],
 {f, 1, 5}, {p, 3, 9}, {fill, {Bottom, Top, Axis}}, {color, Red}]
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Any expression in the Wolfram Language can be manipulated, including non-graphics expressions:

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⨯ 
Manipulate[Expand[(a + b)^n], {n, 1, 20, 1}]
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QUICK REFERENCE: Dynamic Visualization »