Recent content by ericm1234

Is there any website that has a database of physics (or other course) powerpoint slide sets? For example, I am teaching both an introductory physics class, and a separate calc-based physics class of what should be the same general material as the non-calc-based. For the former class I am using...

Thank you for that explanation; How come the definition I have from a functional analysis textbook states it not in terms of bounded maps, but as an isometry?

The context of my question would be taking place in the Hilbert spaces for the example I gave, if someone can comment more explicitly on that; it'd be great if someone can walk through why the "Poisson map", from H^1_0 to dual space of H^1_0, is an isomorphism.

I have read a definition of isomorphism as bijective isometry. I was also showed a definition that isomorphism is a bijective map where both the map and its inverse are bounded (perhaps only for normed spaces??). This does not seem to be the same thing as an isometry. For example, the poisson...

Thanks; do you believe (as in, is it plausible) that the author means: ||u-u_s||/||f||<=eps means that thing less than eps is "of order epsilon"?

Well, that was sort of what I figured..but anyway, Brenner, Mathematical Theory of Finite Element, p.6 bottom. Thanks

I paraphrased for the sake of drawing attention to my (pedantic) question; The original statement, from a book on finite element, was: ||u-u_s||<=eps*||u-u_s||_E <=eps^2*||f|| (the middle norm is energy norm) the following text then goes: "The point of course is that ||u-u_s||_E (energy norm)...

I am trying to reconcile the following statement: " ||u||<=eps*||f|| means ||u||=O(eps) ("||u|| is order eps")... " with the limit definition of "big O"; considering it's not clear that ||u|| here even depends on eps: " lim as eps goes to 0 of ||u||/eps, by definition of "big O", should...

the equations are not derived in the link you gave; my own derivation fails to see where the last terms in those 2nd and 3rd equations in that link are coming from.

Can anyone point me to a derivation of the navier stokes equations in polar? I don't see where the single derivative in theta terms are coming from in the first 2 components.

It is by the definition of "independence" in statistics that E(X*Y)=E(X)*E(Y). If two X's are independent should not E(X^2)=E(X)*E(X) from this context? A bunch of iid X's from say, a normal distribution are independent with each other and yet do not fit the above definition of independence...

I can make up an example to show it's obviously not true; I'm asking for an explanation of the use of the word independent in this context.

Doesn't help because I then need to find E(x^4); I'm dealing with a continuous function, hence my question about trying to avoid integrating. "do the math" doesn't help my understanding. The term 'independent' is used in regards to a series of random variables X from the same distribution and...

1. I know var(x)=E(x^2)-E(x)^2; is there a repeated way to use this to attain var(x^2)? Or how in general, without resorting to integration, can I calculate it? 2. We typically deal with "i.i.d random variables X_i" and do things like find var(X) given E(X^2) etc..it never occurred to me...

well I'd delete my post but I don't see how; for anyone interested, what I failed to see was that in having the 3rd component, the first 2 basis vectors are now (cos, sin, 0), (-sin,cos,0) respectively, leading ultimately to the third term never showing up except as dw/dz. Solved.