5,045 reputation
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bio website mathcs.holycross.edu/~ahwang
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visits member for 9 months
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2h
reviewed Close injection in sobolev space
2h
reviewed Close PDF of Sum of Two Random Variables
2h
reviewed Close probability and applied statics 4
10h
comment A basic question on surface area of spherical cap of sphere
The "elementary geometry" formula for the area of a zone on a unit sphere comes from Archimedes' theorem: $A = 2\pi \times\text{height of zone}$. It appears you (aaaaaa) are using something like the height of the zone times the circumference of the base...?
11h
comment About the branch-cut in the complex logarithm
As you say, $a^{2} + r^{2}\cos(2\phi) < 0$ when $\phi$ is "close to" $\pm\pi/2$. (This is implicit in my "preimage of the cut" remark.) I'm less certain about your remaining comments: There's only one "$\log$" function in this entire discussion; the function $z \mapsto \log(z^{2} + a^{2})$ is defined everywhere except the two imaginary cuts. If you try to use $\log_{L}$ and $\log_{R}$ to indicate limiting behaviors near the cuts, you can't compare $\log_{L}(z^{2} + a^{2})$ and $\log_{R}(z^{2} + a^{2})$, since their domains don't overlap.
22h
revised Find the flux of the vector field across the boundary of the cube
Tweaked LaTeX, added tag
22h
reviewed No Action Needed Find the covariance of estimation error
22h
reviewed No Action Needed $\sum\limits_{n=1}^\infty n(\frac{1}{2})^{n}$
22h
reviewed No Action Needed Dual quaternion inverse
22h
reviewed Close Let $p(t)$ be a polynomial in $\mathbb{R}$. Defining $p_0(t) = p(t)$
22h
reviewed Looks Good Addition of Sets which isn't union
1d
comment Interesting calculus problem advice
@Awesome: Looking at simpler cases is "Polya's good advice" and "a customary method of solution", not "cheating a bit". ;)
1d
comment Interesting calculus problem advice
@Awesome: Try looking at "simpler limits of the same form": fewer exponentials in the towers, correspondingly fewer terms in the round parentheses.
2d
answered Interesting calculus problem advice
2d
reviewed Close Whats wrong with my Matlab user defined taylor function ??
2d
reviewed Close A seemingly basic PEMDAS problem…
2d
reviewed Close Computing joint probability
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reviewed Close Are all polynomial-bounded functions computable?
2d
reviewed Close How do I approximate cos(0.1) to two-decimal using a Maclaurin series?
2d
reviewed Close how to find a series of r.v. which is not complete convergences but a.s.