Recent content by pellman

Thanks, guys. I will think it through some more.

I think my trouble stems from the definition of one-forms as linear maps from a tangent space to R, which seems to have nothing to do with infinitesimal changes of a real variable. Is there another equivalent definition of one-forms?

My understanding of it is not very deep. Just an infinitesimally small change that results in a linear change in the dependent function.

Thanks for that link.

If H is a vector field and dx is one from, what is H dx? But I don't know that it matters to my question. What I am looking for is a conceptual bridge between the two types of mathematical objects. What was it about differential forms in the early days of the subject which led...

Right but I don't see it. Hence the question.

Why are n-forms called differential forms? What is differential about them? And why was the dx notation adopted for them? It must have something to do with the differential dx in calculus. But dx in calculus is an infinitesimal quantity. I don't see what n-forms have to do with infinitesimal...

Thank you!

I just now got an email notice about the reply above. I guess the forum email program is a year off? Anyway, I'd still be interested in replies to this thread. Greg's reply doesn't really help. What happens to a continuous charge density? A reference to a source that covers the equation of...

I understand this now. If anyone wants an explanation, reply here and I will explain.

The definition of the hermitian conjugate of an anti-linear operator B in physics QM notation is \langle \phi | (B^{\dagger} | \psi \rangle ) = \langle \psi | (B | \phi \rangle ) where the operators act to the right, since for anti-linear operators ( \langle \psi |B) | \phi \rangle \neq...

Thanks, fresh_42

The specific problem is to show that ## x \sum_{p=1} ^\infty \ln \left( \frac 1 { 1 - e^{-p/x}} \right) ## approaches ## \frac { \pi^2} {6} x^2 ## for large x. So we could drop the leading x and just show that the sum is linear for large x. I know that the pi^2 / 6 comes from ##...

I have a problem asking to show that a certain function approaches a quadratic for large values of the variable. And I realize now that this is a skill with which I am totally unfamiliar. Can't use a Taylor series in y= 1/x because the value at y=0 is infinite. Would appreciate a recommended...

There are two strangely mirrored but opposite assumptions here. On the one hand, stochastic independence amounts to saying "If we made a series of measurements to get the distribution of velocity components along one axis, it gives us no information about the distribution along orthogonal...