Recent content by the.bone

Thanks for the author reference, I will try to make it to the library tomorrow. Cheers! PS: I found a few online references, including the one you pointed me to, but the underlying theme seems to be to have a bunch of chit-chat with very little / no math, hence why ended up posting here...

Hi all! OK, hopefully this will be a very quick question. Basically, I want to know how to model a vacuum tube (both triode and pentode) in terms of creating a dynamic system model. For example, if were to look at the voltage in an inductor as a function of time, I would employ the relation...

Recall that: R_{ijkl}=\dfrac{\partial \Gamma_{ijl}}{\partial u^k}- \dfrac{\partial \Gamma_{ijk}}{\partial u^l}+\Gamma^h_{ik}\Gamma_{jhl}-\Gamma^h_{il}\Gamma_{jhk} So that: R_{1111}=\dfrac{\partial \Gamma_{111}}{\partial u^1}-\dfrac{\partial \Gamma_{111}}{\partial...

Thanks! I think... If I understand you correctly, the above notation, then, is somwhat abusive in that typically, a pairing is usually between an element of one space, and something that is dual to it, like \left<\dfrac{\partial}{\partial x},dx\right> Not an iron fisted rule, mind you, but...

I would HIGHLY recommend "The Theory of Matrices" by Lancaster et. al. I'm not too sure if it's even in publication any more, but it shouldn't be too hard to get a used copy--there's one at powells.com for only $22 right now! Get it!

OK, this is more of a spot for an elaboration on a question I just posted in another thread. Not quite duplicating threads, I hope, I just wanted to have this not buried in another spot... So, the question is this: Let's say that we have a smooth manifold \mathcal{M}that may be viewed as a...

***UPDATE*** OK, so here's where I'm at. We can, with some trickery, view the action of the laplacian on a function on a Riemannian manifold as \Delta f = \dfrac{1}{\sqrt{\det g}}\dfrac{\partial}{\partial x^j}\left(g^{ij}\sqrt{\det g}\dfrac{\partial}{\partial x^i}f\right) and we also can...

Well, I don't think so... As I understand it, the Laplace-Beltrami equation is merely a generalization of the Laplacian as it applies to taking the laplacian of a k-form on a manifold. What I am after is how to perfom the specific acrobatics to get from the "regular" heat equation to the...

The Geometric Heat Equation--WTF?? I need some help getting from point A to B. Let's say we have the plain ol' heat equation u_t=\Delta u where the u=u\left(x,t\right), and that's all good. Then, we also have the so-called geometric heat equation \dfrac{\partial F}{\partial t}=kN where...