One for JimC ...

[Calilasseia]

I recently encountered something you might be interested in, Jim. The Lambert W function. Now there's something to torment your calculus classes with.

[JimC]

I just looked it up on Wiki - fascinating, but it made my head hurt. Very interesting example of using colour to show how the function(s) behave on the Argand Plane...

Definitely uni level material - our guys doing the full maths course certainly delve into complex numbers and inverse relations, but that exemplar, containing both, would be a bridge too far. This summer, I should take 3 or 4 examples like this, of branches of maths I have never explored, and see if I can get the hang of them properly.

Thanks for the heads-up!

[pErvinalia]

Geeks.

[JimC]

Beware Geeks bearing gifts...

[Calilasseia]

I'm congratulating myself on having worked out how to derive the differential equation and the integral from first principles.

[Clinton Huxley]

The long winter evenings must just fly by

[Xamonas Chegwé]

I'm congratulating myself on having worked out how to derive the differential equation and the integral from first principles.

By "the differential equation" I am assuming you mean derivative?

Deriving the derivative of a polynomial from first principles is pretty simples. Trig functions range from tricky to "How the fuck did anyone think of doing it that way?!!"

Similarly with integrals, although they are, in general, ALL quite a bit tougher.

[Calilasseia]

Trouble is XC, you're not dealing with a polynomial here. You're dealing with a function in the complex plane that has no closed form representation in the independent variable. And what's more, unless you know the tricks, it's a bastard to handle.

[Xamonas Chegwé]

Trouble is XC, you're not dealing with a polynomial here. You're dealing with a function in the complex plane that has no closed form representation in the independent variable. And what's more, unless you know the tricks, it's a bastard to handle.

Oh, you're still talking about the W function.

[pErvinalia]

Geeks.

[mistermack]