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10 October, 2013

Mathematica Manipulate[] example

Addendum to the Mathematica 101 post. I was working today and noticed that this little device is fun to use, and thus wanted to post it. Variable names have been changed to protect the innocent. I might even add more to this post in the future...

This is what I do often with Mathematica, I have some data computed/acquired somehow and I want to look at it from a few angles and try to find an analytic expression, without knowing all the underlying math, because either it's too hard to find a closed solution or I'm just not good enough.
Anyhow finding approximations even on paper would require assumptions that you have to check anyhow, and a good way to check them is to compare with the computed/acquired data. Other times you know a perfectly find analytic expression but want to fit a second one that's cheaper to compute.

With Manipulate is easy to explore a parametric function, given one. But most often I'm not entirely sure of the parametric form to use to begin with! Fear not, as in Mathematica everything is an expression, of course you can Manipulate expressions as well...

The code and graphs are captures in the two screenshots below, click on them to see the original size.

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