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Story time📖 (1/3)
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.
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.
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..
👉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..
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 wonderful
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 wonderful
