Recent content by subsonicman

Yeah, I was being stupid. Thanks for the help!

Today I tried to show that rotational kinetic energy was equivalent to standard translational kinetic energy. So I started with kinetic energy, T = ∫dT. Then, because T=1/2mv^2, I substituted dT=1/2v^2dm and then because m=ρV, I substituted dm=ρdV. Then, after substituting v=ωr, I got the...

@Micromass I'm fairly sure for the first function ##\inf(U(f,P_n))=0##. A non-rigorous proof is as follows: Let's say we want to find ##n## such that ##U(f,P_n)<\frac{1}{m}## Note that there's only a finite number of rationals ##x## such that ##f(x) \ge \frac{1}{m}##. Each of these can only be...

It's really hard to tell. I thought it was obvious earlier but I was only thinking of the values of the function at the end points.

There are two things I can think of. One is an example they use a lot in the book which is 0 for irrationals and 1/q for a rational with p/q in lowest form. But the upper bound can be arbitrarily close to 0 for equal partition. The second is let the value be 1 for all rationals of the form 1/m...

That function f isn't integrable. Since in every interval there is some x so f(x)=1 and some x so f(x)=0, the upper sum is 1 and the lower sum is 0.

This is spivak's calculus 2nd edition #12b. The question in part a defines Pn as a partition of [a,b] into n equal intervals. The question in part b states: Find an integrable function f on [0,1] and an ε > 0 such that U(f,Pn)-∫0 →1 (f) > ε for all n. I'm made no progress on this at all. Part...

I just rewrote the thing in the link to only include the part I was having difficulty with. $$ \sum_{n = 0}^{\infty}\frac{1}{2^{n+1}}\frac{n}{n+1} = \sum_{n = 0}^{\infty}\frac{1}{2^{n+1}}\left(1 -...

I was looking at this topic: http://mathoverflow.net/questions/17960/google-question-in-a-country-in-which-people-only-want-boys-closed And the top answer uses the fact that the sum from 1 to infinity of 1/(x2^x) is log 2. Why is this true? Thanks in advance.

I've been reading through Spivak's calculus, and the problem is the answer key i have a hold of is for a different edition so it often doesn't answer the correct questions. Anyways, here they are: Chapter 5 problem 10 b. Prove that lim x-> 0 f(x) = lim x-> a f(x-a) c. Prove that lim...

Oops I'm sorry, I meant to say momentum, thanks for the catch.

I recently learned that a free electron can't absorb a photon and derived it by showing it would be impossible to conserve both momentum and energy if that were the case. It seems like the same argument would extend to other fundamental particles. Is it true that no free fundamental particle can...

I was reading this page: http://en.wikipedia.org/wiki/Tensor which said the definition of a tensor was a relation between two vectors. I then went down to the examples section and it had some sort of (n,m) notation. I had some theories on what they meant but none of them made sense. What do n...

Homework Statement A photon of Energy E_0 collides with a free particle of mass m_0 at rest. If the scattered photon flies off at angle θ, what is the scattering angle of the particle, β? Homework Equations The relevant equations are conservation of momentum in x and y direction and...

I guess you guys have convinced me to hold off on a comprehensive work on multivariable until after I've learned linear algebra. My plan now is to just get a general overview of the stuff I don't know in multivariable over winter break, using some easier book. While I love exploring math for its...