Recent content by J Hill

Well, there are a lot of ways to conceptualize entropy, based on how the math works out, but when it comes right down to it there is one strict definition of entropy, S: S = k_B \log \Omega, where kB is Boltzmann's constant (~1.38×10−23 J K−1) and Ω is what is called the multiplicity-- what...

Okay, so given a family of orthogonal polynomials under a weight w(x) is described by the differential equation Q(x) f'' + L(x) f' + \lambda f = 0, where Q(x) is a quadratic (at most) and L(x) is linear (at most). with the inner product \langle f | g \rangle \equiv \int_X f^*(x) g(x)...

Sometime last year, I wrote a textbook on introductory E and M. In one of the chapters, I attempted to solve the Lorentz equation for a charged particle moving in an arbitrary magnetic and electric field, that I'm not so sure about. Is anyone, who has some experience with solving systems of...

I've recently begun to study continuum mechanics, and am having difficulty with tensor derivatives, primarilly because of notation... so can anyone explain what these equations mean, as far as notation goes: 1. \frac{\partial f}{\partial\mathbf{v}}\cdot\mathbf{u}=Df(\mathbf{v})[\mathbf{u}] 2...

There is a technique called exponentiation (I think) used to solve these types of equations. Just put both sides of the equation in an exponent that is the same as the logarithm base, like this: 2^{log_{2} (x+2)} =2^{log_{2} (x^2}} Then you can use the rules for logs an exponents to get to...

Well, you what you need is: L_{B0}+ \Delta L_{B} < L_{R0} +\Delta L_{R} All that should be necessary is to substitute in the expression for thermal expansion. Where the B values are for the steel ball, and the R for the brass ring/surface

Okay, I have done some work with this before, but if I'm wrong, I hope someone else can correct me. When two objects collide elastically, they naturally compress and kind of stick together momentarily. In this case, the collision acts like an inelastic collision, which causes some of the energy...

Have you done free-body diagrams in your class? If not, think of the couch as a point mass and label all of the forces on it. ...^ ...| Fn ...| fs <----o----> Fa ...| ...| W ...v (sorry, just did this quickly) These help sort out which forces you're looking at. Secondly, the...