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Jul
15
awarded  Commentator
Jul
2
comment Calculating euler number of disk
$t^{a}\nabla_{a}t^{b}$ is a vector. you could write this as $\left({\vec v}\cdot {\vec \nabla}\right){\vec v}$. How on Earth are you working through Polchinski if this is over your head?
Jul
2
comment Calculating euler number of disk
@user238194: for your first question, I'd project your first expression into tangent and normal components. For your second question, what is the boundary of a hemisphere? What do you know about geodesics on spheres?
Jul
2
comment Calculating euler number of disk
Is your manifold a disk in 2-dimensional flat space? For a d dimensional submanifold of a D dimensional space, you generically have $D-d$ normal vectors and $d$ tangent vectors.
Jul
2
comment Calculating euler number of disk
@user238194, not if $n_{a}$ is the unit outward normal. In 2d, this is $n_{a} = (x/r)dx + (y/r)dx$, which does not have zero derivative.
Jul
2
answered Calculating euler number of disk
Jan
21
revised Can $1\over 1$, $1\over 2$, $1\over 3$, $1\over 4$, etc. be calculated by the added fractions below?
expanded answer
Jan
21
answered Can $1\over 1$, $1\over 2$, $1\over 3$, $1\over 4$, etc. be calculated by the added fractions below?
Jun
10
comment Expanding the integrand gives a different result
Oh, duh. Yes. Shouldn't math in the morning.
Jun
10
comment Expanding the integrand gives a different result
If you expand the exponential in $\beta$, doesn't that whole term become $\frac{1}{\beta \hbar \omega}$? I don't obviously see why the integral of $\frac{\sin(s\omega)}{\omega^{2} + \gamma^{2}}$ is zero.
May
7
comment Adding sin(x + a) + sin(x + b)
I will say that choosing those particular points is potentially not optimal. The key is to get the sine to take known values. It might also be prudent to shift your overall equation before you start, so you can eliminate $a$ or $b$, i.e., by defining $z = x+a$, and then defining $\beta = b -a$, and $\delta = d - a$ so you have fewer constants to worry about.
May
7
comment Adding sin(x + a) + sin(x + b)
@mafutrct: I have to admit that it's been years since I've done this, but I have solved this identity this way when proving circuit results to class.
May
6
answered Adding sin(x + a) + sin(x + b)
Mar
15
awarded  Yearling
Feb
8
comment Replacing large-dimensional ODE systems with one PDE
@SergioParreiras: see edit.
Feb
8
revised Replacing large-dimensional ODE systems with one PDE
added 444 characters in body
Dec
18
awarded  Supporter
Apr
2
comment computing the $y_{cm}$
Also, I would recommend not carrying around your denominator. What should your answer for $\int dm$ be?
Mar
26
answered Replacing large-dimensional ODE systems with one PDE
Mar
1
comment Change of Variables in a 3 dimensional integral
Hint: try calculating the volume of a sphere in Cartesian and in Spherical coordinates.