Jerry Schirmer
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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.