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Jan
9
comment Machine limit analysis of $\sqrt {x^2-a^2}-(x-a)$
You mean you want an answer not just a hint?
Jan
6
awarded  Citizen Patrol
Jan
6
comment jordan canonical form with direct product?
Nice answer! I'm curious, do you happen to know a source where the connection between the exterior product of matrices (or linear transformations) and the cofactor expansion is explicitly given.
Jan
6
comment jordan canonical form with direct product?
my naive viewpoint is that $f \otimes f$ is simply formed by sticking $f$ in each component of $f$. It is a $9 \times 9$ matrix. The $\Lambda^2 f$ is likely an antisymmetric object based on $f$, but, I'm not certain, do you have a reference?
Jan
5
comment Super conic sections?
Curious, you might try asking some questions about your construction once you have something a bit more precise. You might find interest.
Jan
5
comment Divergence theorem in complex analysis
No problem, I'm curious, did you have a course in several complex variables at some point? If so, what's a good book to read... lately I tinker in calculus of an associative algebra, I will admit, I don't know too much about complex variables in particular...
Jan
5
comment Super conic sections?
@tox123 Interesting, I have not managed to get the 3D stuff in Desmos to look that nice. Good work.
Jan
5
comment Divergence theorem in complex analysis
Intuitively, I thought $dS$ would be $d\theta$ for the circle.
Jan
5
comment Divergence theorem in complex analysis
I agree. But, Ted has me worried there is more...
Jan
5
comment Divergence theorem in complex analysis
Oh no. Shall I delete the answer...
Jan
5
answered Divergence theorem in complex analysis
Jan
5
comment Divergence theorem in complex analysis
will do. .......
Jan
5
comment Divergence theorem in complex analysis
Are you sure $r$ has length $1$? I think the $r$ is really $r^2$. Hence, in less awesome notation, $\nabla r = \langle 2x,2y \rangle$ which has length $2$ on $x^2+y^2=1$. Nothing else pops out as wrong except that point, the $r=|z|^2-1$ has $\nabla r$ of non-unit length. So rescale by $2$ and it's spot on.
Jan
5
comment Complex integration $\int_{-\pi}^{\pi} \frac{\sin^2 t}{3+\cos t}dt$
I think this is an integral you want to convert to a $z$-integral to use Cauchy's formula or the residue calculus. The point is to identify the integrand as the parametrized form of a particular contour integral, it is not as you attempt it I think. See Section 7.3 of supermath.info/GuideToGamelin.pdf for examples of the technique.
Jan
5
comment Super conic sections?
Notice, there is a picture of a cubic curve in the linked article. Also, I do think many curves in the plane can be obtained by intersecting surfaces in 3D, that would be the generic analog of planes intersecting a cone. Not too exciting, but that's my initial thought on your query.
Jan
5
answered Super conic sections?
Jan
4
comment Super conic sections?
what happens is we know not so much up there.
Jan
3
comment $\arccos(i)=z$ (Complex Variables)
Those two answers are implicit within his $\pm$ on the $\pi/2$. The $+$ gives your answer, the $-$ gives the $3\pi/2$. This is typical of a trig. equation, we tend to get two sequences of answers which are separated by $2\pi$. Graphically, it's not too hard to visualize in the real case. Think about a horizontal line intersecting a sinusoidal graph. It hits the wave the same two spots every cycle...
Jan
3
comment $\arccos(i)=z$ (Complex Variables)
But, $-\pi/2+2\pi = 3\pi/2$. I think his answer has $3\pi/2$ and much much more...
Jan
2
comment Subspace for a matrix representation of a linear transformation
Notice, there is no condition on the $B$ or $C$ matrices, so those columns of the matrix don't really say much except that $v_{k+1}$ to $v_n$ map to a span of $\beta$.