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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.
Feb
13
comment Divergence theorem on Hyperbolic space
@PML: it works in both cases. The minkowski case is cleaner, since the $r,\phi,\theta$ system is orthonormal in the minkowski case. If you embed in Euclidean space, though, you will still find that $\sqrt{\rm det g} = r^{2}\sinh\phi d\theta d\phi$, you'll just have to content with $g_{r\phi}$ components to your metric tensor.
Feb
12
awarded  Editor
Feb
12
revised Divergence theorem on Hyperbolic space
added 8 characters in body
Feb
11
awarded  Teacher
Feb
11
answered Derivative of a factorial
Feb
11
answered Divergence theorem on Hyperbolic space