Isn't that integral really similar to the normal distribution?
Substitute x^2 for k^2/2 => x = 2^-.5*k
Then you have the normal distribution without the usual normalization constant of 1/(2 pi)^.5,
So that integral should be equal to... pi^-.5. Assuming I did my math correctly. (if the...
Okay, so this obviously isn't as interesting as I thought...
A general transformation of a function f(x,y) to f(z) is still eluding me. That's unfortunately the key to making this idea more general.
If I remember correctly, all conservative forces are central, meaning they can be written as...
I'm having trouble implimenting the transformation for this. I thought I understood it in concept: make the y-axis the imaginary line and the real-line the x-axis.
Essentially that would mean: f(x,y) = f(x, iY) and then use x + iY = z, where iY = y.
That's not very easy though... is there...
Preface:The best way I've been taught how to prove that a force is conservative is to take the curl of the force and show that it is equal to zero. That's pretty quick, but after studying for a complex analysis midterm this idea struck my mind. I'm not a master of complex analysis, so there...