Recent content by mathnerd15

well say you could create a vector particle whose integral from 0 to infinity would be 1 unit vector :) this seems to be a powerful technique for instance to discretize a space...

wow Susskind is amazing, I was wondering too how small can you reduce a unit basis vector, maybe to the size of a differential? I guess very few people have the talents to become theorists?

is there some contradiction where localized logical inferences don't hold true in other cases?

so Rn is clopen because its complement the null set is open so it can be closed, while you can construct an open ball from any point which is interior to the set so that S=Int(S), all points are interior to the set since +- infinity aren't included in Rn? is the null set really open since it...

Apostol Limit Problem? Homework Statement I can't afford the Apostol calculus vol. 2 there's a printing mistake in my copy of Apostol and I'm not sure how to prove this, p.251 let f(x,y)={xsin(1/y) if y doesn't equal 0 and f=0 if y=0 prove that the iterated limits are not equal and that the...

when you solve a 2nd order linear non-homogeneous DE, where it is equal to a constant as in Kirchoff's 2nd Law and the roots of the auxiliary equation are imaginary then you have superposition of 2 solutions. so the particular solution is equal to a constant k and you can solve for this by...

I was just wondering about these indices in the Apostol copy I have. so it includes an introduction to metric spaces and topology?

can you prove minimally that a set is open if its complement is closed or that a set is closed if it contains all of its limit points? what are some of the more beautiful and advanced uses of open sets?

I really love Apostol, it is at a higher level than Stewart

there are really some genius level people doing amazing work in mathematics and physics. I wonder if you need pure talent to do algebra and calculations in your head. I kind of feel the same way, I'm working on Griffiths problems and it takes time, but I still have a passion for it and it's...

so since Laplace says that there can be no local extrema then a charge at the center of a cube with charges at the 6 corners cannot be in electrostatic equilibrium since then U would be at a minimum? if the potential is like a saddle point for the center charge in a cube then in the xz plane it...

is fuel cell, energy research a good field that is well funded? it seems there would be more funding for biomedical engineering, medical applications like medical physics, radiology/imaging, proton beam therapy, nanoparticle pharmaceutical research personally I love pure mathematics but it's...

I wonder if one should study books like Gauss's General Investigations on Curved Surfaces or Euler's works or there are more modern texts that are state of the art?

thanks very much! assuming superposition for potentials is true as with E fields...where q1 and q2 are the charges of the rings respectively and Q is the charge moved from infinity. V=\frac{q1}{4\pi\epsilon oR}+\frac{q2}{4\pi\epsilon o(\sqrt{2}R)} \\ q1=\frac{4\pi \epsilon o...

the center of the rings of radius R are on the x-axis a distance R apart from the centers of the rings Ex=\frac{Qx}{4\pi\epsilon o(x^2+R^2)^{3/2}}-\frac{Q(R-x)}{4\pi\epsilon o((R-x)^2+R^2)^{3/2}} perhaps it's better to do the calculations in more complexity. is this correct for the expression...