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 Yearling
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Jun
17
comment How to compute this integral involving sech?
What have you tried? (And is $\epsilon$ "small and positive"?)
Jun
17
revised How to compute this integral involving sech?
Updated TeX formatting slightly
Jun
17
suggested approved edit on How to compute this integral involving sech?
Jun
17
comment Question on $\mathfrak{sl}(2,\mathbb R)$
@PeterFranek, could you remind me why it's not a group? I thought it was a subgroup (since it has the identity element and the Baker-Campbell-Hausdorff formula suggests it is closed under multiplication, right?) but rarely is it the full group...am I mistaken?
Jun
8
comment Intuition behind the definition of a derivative by Lang
Maybe it's because I'm drunk, but isn't the $\lambda y$ term merely the linear term (i.e., derivative) and $\varphi(y)$ the "bonus parts which vanish in the appropriate limit"? Just as if for a usual function in calculus 101 we would Taylor expand $f(x+h)=f(x)+f'(x)h+g(h)$ where $g(h)\sim o(h^{2})$. The derivative would naturally be the linear (first) term...well, the coefficient to $h$...
May
18
awarded  Yearling
May
11
comment What's the term for a “physical vector space”?
@RobertIsrael perhaps use the "accountant's trick" and let negative fruit be a deficit owed to someone, and fractional fruit be a fraction of a fruit? (It works in Sraffian economics!)
May
9
answered Identifying a power series
May
3
comment How would you evaluate $I:=\int_ {0}^{\infty} \frac {\cos(ax)} {(x^2 + b^2)^n} \ \mathrm{d}x$?
Consider the real part of the integral $\int(x^2+b^2)^{-n}\exp(iax)\,\mathrm{d}x$ might help...
Apr
22
comment What's the name of this category
Isn't it isomorphic to the category $C_{A\times B}$?
Apr
20
awarded  Organizer
Apr
20
revised Why the $\zeta$ letter is like this?
Fixed tags
Apr
20
suggested approved edit on Why the $\zeta$ letter is like this?
Apr
20
comment Link between a topological space and a manifold
The topology is the collection of open sets of the space (by definition, a member of the topology is called an "open set"). But when a manifold "locally looks Euclidean", you're talking about charts...the image of a chart is itself an open set in the manifold, which requires a topology to talk about...
Apr
20
comment Why the $\zeta$ letter is like this?
@Goos, the difference is really negligible. Once you get one method of writing a zeta, it's not terribly difficult to deform the orthography into the one you desire. But starting with some zeta, I found, has been the hard part (for me anyways).
Apr
20
comment Why the $\zeta$ letter is like this?
foundalis.com/lan/hw/grkhandw.htm
Apr
18
awarded  Civic Duty
Apr
15
comment Solve $\sqrt{1+\sqrt{1-4x^2}}=x\left( 1+\sqrt{1+\sqrt{1+2\sqrt{1-4x^2}}}\right).$
Perhaps set $u=\sqrt{1-4x^{2}}$, so $x = \sqrt{1-u^{2}}/2$ and the problem becomes $2=\sqrt{1-u}(1+\sqrt{1+\sqrt{1+2u}})$...?
Apr
11
revised Evaluate $\int_{0}^{\pi/4}\frac{6 - 6\sin^{2}(x)}{2\cos^2(x)} \mathrm{d}x $
Improved the tex formatting
Apr
11
suggested approved edit on Evaluate $\int_{0}^{\pi/4}\frac{6 - 6\sin^{2}(x)}{2\cos^2(x)} \mathrm{d}x $