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Homework Statement I want to integrate the 2-form defined on R^3\{0,0,0} over the unit sphere. (x/r^3)dy wedge dz+(y/r^3)dz wedge dx+(z/r^3)dx wedge dy Homework Equations r=\sqrt{x^2+y^2+z^2} The Attempt at a SolutionI'm thinking this is like a surface integral but I'm not really...

I filled out some of my reu applications by hand rather than typing them up on the computer. My parents don't think this is acceptable. What do you guys think?

Help with physics REU statement of interest! I've been working on this for several days and it just comes off as so blah and uninspired to me. I'm a bad writer and I haven't written an essay in 7 months so I'm having trouble wording things the way I'd like. Please critique what I have so far...

Does g(x)=the characteristic function defined on the interval (0,1] work?

Anyone?

f is continuous except at a finite number of points where it is discontinuous.

Yeah, I guess that's true. Darn it...back to the drawing board. Anyone have any suggestions as to what would work?

Compositions of functions and integrability (is this right?) Homework Statement We know that if f is integrable and g is continuous then g\circf is integrable. Show to this is not necessarily true for piecewise continuity. We are given the hint to use a ruler function and characteristic...

Thank you both for your quick and helpful replies.

Homework Statement Given characteristic functions f and g on the intervals [1,4] and [2,5] respectively. The derivatives of f and g exist almost everywhere. The integration by parts formula says \intf(x)g'(x)dx=f(3)g(3)-f(0)g(0)-\intf'(x)g(x)dx. Both integrals are 0 but f(3)g(3)-f(0)g(0) is...

My professor gave me the following hint and I think I can figure it out from here. I just want to know why M and N are homeomorphic. It is not in any of the theorems in the book. There is a theorem that says if M is homeomorphic to N and M is connected then N is connected. "I think that this...

This sounds bad but I'm still confused about how to construct the function. I'm running into issues when I take the composition of 2 straight lines with constants turning into variables.

What if you went to some (i1,c) where c is irrational and then to (i2,c) and back to (i1,r1)?

Oh crap I didn't think about that.

My friend's bf often proofreads her papers. She asked him what he thought of one and he said it was "ok". She had a hissy fit over this until she got him to tell her it was great.