Recent content by lus1450

Yes I do know them. For whatever reason, I decided to try and ask the question as if I were a student to somehow gain some hints about to explain things to them. I'm still new to the process, but perhaps I should be more up front in my motives from the start.

Ah yes, I can break it up into ## \frac{1}{x} ## and ## \frac{1}{(\sqrt{1+\frac{1}{x^2}} + 1)} ## the former having a limit of 0 and the latter having a limit of 1/2. In this way, I can "leave the former limit alone," obtain 1/2 from the second one, and then recombine it back into ##...

Homework Statement Find \lim_{x\to \infty} \sqrt{x^2+1}-x Homework EquationsThe Attempt at a Solution This is mostly for a refresher. I know it's zero because when we multiply the top and bottom by the conjugate to obtain \frac{1}{\sqrt{x^2+1}+x} and the denominator increases without bound...

I will be starting a PhD next month. I know there are other things I need to worry about (actually getting through the next 5 years for one), but I would feel a bit more at ease if I discussed this before hand. First off, I'm pursing the degree because I love math and hope to be a professor...

Thanks for the reply. To expand on this, what is a good metric to finding a "well known" professor at these schools? I've recently been searching their names through the arXiv and the Genealogy Project, but I'm not sure if that tells me anything since having papers uploaded there doesn't mean...

Thanks for the reply. I'm from California, so I'm not sure if you're familiar with California State system. Even though none of them are "ranked" I do see that there quite a few professors from top schools and quite a few from mid rank schools. So even schools like that seem some what...

I'll be applying to PhD programs in pure math this fall. However, my profile isn't that outstanding, so I'll most likely being going to a "mid" to "low" rank (as determined by US News Grad Rankings, for what it's worth). Ultimately, I'd want to do research as well as teach lower/upper division...

Alright, so then your R goes from H to the unit square?

Well the thing is, nothing went wrong per say, but there was a dispute in office hours about whether it was applying ##T## or ##T^{-1}## to the region/integrand, and the majority was on the side of applying ##T##, but it just didn't make sense to me as to why. So, applying ##T^{-1}## is correct...

Thanks Mark44. I mean, I get you want to apply it to BOTH region and integrand, but I'm not sure why applying T to H would give me the integral over the unit square, as T is from the unit square to the parallelogram. In my lower division calculus, when we learned about this, our...

Homework Statement Let ##H## be the parallelogram in ##\mathbb{R}^2## whose vertices are ##(1,1), (3,2), (4,5), (2,4).## Find the affine map ##T## which sense ##(0,0)## to ##(1,1), (1,0)## to ##(3,2), (0,1)## to ##(2,4)##. Show that ##J_T=5## (the Jacobian). Use ##T## to convert the integral...

Ah okay, thank you! I just realized I was swapping linear transformation and matrix in my thought process, since in my linear algebra class "A" is normally a matrix while in my analysis class, "A" is a linear transformation. As such, it is saying A(h), not A*h. My confusion is cleared up =]

Homework Statement Let ##f: M_{n \times n} \rightarrow M_{n \times n}## with ##f(X) = X^2##, where ##M_{n \times n}## denotes the vector space of ##n \times n## matrices. Show ##f## is differentiable and find its differential. Homework Equations The Attempt at a Solution So far...

Homework Statement Find the meridians and circles of latitude of a surface of revolution ##X(t, \theta) = (r(t)cos(\theta), r(t)sin(\theta), z(t))##. Homework Equations The Attempt at a Solution I honestly just need a definition of what these concepts are. My book, as an aside for...

Oh okay, that's a good idea, thanks. Are these generally free for people to just walk in? We have IPAM at my school, but it lists fees for Faculty, grad students, etc. but no undergrads.