By Gerd Baumann

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The Manipulate function allows us to dynamically change the parameter a and watch the graph of the corresponding cubic polynomial change! This book, of course, is totally static! You have to try this out for yourself with Mathematica! 3 The expanded slider control. Notice that the output cell contains the graph of the function together with a slider control labeled “a”. As we drag the slider control with the mouse we change the value of a and thus change the function and hence its graph. This is awesome!

Try computing 510000000 . This calculation should last long enough for you to see the title of your window change to include “Running . . ” This would be a great place to use a semicolon to suppress output! It is also a great place to use the Timing function so that we can CHAPTER 1 Getting Started 17 see how long the calculation takes. The Timing function can be wrapped around any other calculation. Here is an example. 17752 seconds on the authors’ laptop. The “Null” (which means “nothing”) is present because we used the semicolon to suppress the output.

We have already seen one example of this with the mouseover effects made possible with the Tooltip function. The Manipulate function also allows the user to interact with graphics (and other things too) in a really neat way. Suppose we want to understand the cubic polynomial x 3 + ax + 1, where a is some constant. In particular, maybe we want to know how the value of a affects the graph. We could start picking various values for a and then plot the graph for each value that we have chosen, but a better way is to use Manipulate.

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