Story time
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As an undergrad, I remember seeing the proof for the antiderivative of sec(x).
The key of the proof is to cleverly multiply by sec(x)+tan(x)/sec(x)+tan(x), and pop goes the weasel.pic.twitter.com/Y0iIzvBFFR
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So I started to play around and realized that this factor we multiplied by actually fulfilled a specific property.
sec(x) + tan(x) returned itself times sec(x)
I gave this property the name "quasi-eigenfunction"
I wondered if this could be applied in more general settings..pic.twitter.com/QN1U2FWXxE
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A year later I got to differential equations. The professor showed that what I called quasi-eigenfunctions is called an integrating factor, and spoke about its use. When I found this out, I felt a bond of sorts to past mathematicians; a kinship over centuries. It was wonderfulpic.twitter.com/pZ8h9iaPZx
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I have to teach my calculus students how to integrate sec(x) pretty soon, maybe this week. It's a bit traumatic since it must make them think "how the hell could anyone have guessed that?"
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That's true.. I know there's another way, but it's probably more traumatic. Write cosine as complex exponentials --> u=e^{ix} --> partial fractions.. Yea, they'll love that.
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I'm teaching ODEs this summer, we're doing this on Thursday :D
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you should tell your class to follow me on twitter
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Have you done greens functions yet ?
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yup, sure have.
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That’s really cool.
Thanks. Twitter will use this to make your timeline better. UndoUndo
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Ahead of your time ^.^
Thanks. Twitter will use this to make your timeline better. UndoUndo
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