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No, his mind is not for rent
to any god or government.
Always hopeful, yet discontent.
He knows changes aren't permanent,
but change is.

— Rush, Tom Sawyer


Taking an externally-imposed and much-needed break from SE activities.

E-mail (flipped ROT13): zqd˙ʎʌuzʇ@ʇɐʌǝɥʇʌssqɹǝɥɟuɹʎɔ
Any code I've posted here I place under the WTFPL.


Aug
19
comment Help in getting the Quadratic Equation
A note on the TeX subscripts: try "x_{1,2}". As for the derivation, are you already familiar with "completing the square"? Otherwise, one thing you can try is to make the substitution $x=u-\frac{b}{2a}$, solve for u, and then reexpress the whole mess in terms of x. Good luck!
Aug
19
comment Blow up of a solution
On the other hand, there's books.google.com/books?id=cXH3wTwmygQC&pg=PA3 ; as already mentioned, it has a lot to do with hitting a singularity while going through the mesh of a PDE's approximate solution.
Aug
19
comment Blow up of a solution
Katie: "that a solution (to a pde (say)) blows up" Granted, he neglected to capitalize...
Aug
19
comment Blow up of a solution
Qiaochu: not really that technical I'm afraid; it's much like the concept of "stiffness" for ordinary differential equations: nobody really has a rigorous definition, but people know it when they solve an ODE numerically.
Aug
19
comment Blow up of a solution
Hmm, my understanding of "blow-up" in the context of partial differential equations is that is what happens when, due to singularities inherent in the set of solutions to a PDE, inaccuracies in the approximate solution appear when attempting to approximate the solution with a mesh. Usually this is because the user of the algorithm for solving the PDE may have failed to use the proper dependent variables, neglected to factor out singular behavior, or any number of other things.
Aug
19
revised Solving very large matrices in “pieces”
silly me, it's a vector, not a matrix!
Aug
19
revised Solving very large matrices in “pieces”
additional information
Aug
18
comment Solving very large matrices in “pieces”
Hmm, there were new comments as I was typing this out; so the first formula would be the one applicable to you. It is up to you on how you will organize the computation of subexpressions in your code, just remember to partition your right hand side conformally with the matrix.
Aug
18
answered Solving very large matrices in “pieces”
Aug
18
comment $0/0$ limit question
Robin, we should probably be asking Kokoloko if he already understands the reasoning behind switching to polar coordinates...
Aug
18
comment $0/0$ limit question
I mean a surface plot. You can use something like fooplot.com/index3d.php
Aug
18
comment $0/0$ limit question
Kokoloko: Have you tried plotting the functions you're trying to take limits of? It might help you in understanding why the limits behave the way they do.
Aug
18
comment $0/0$ limit question
Oh, you don't have to worry about me not appreciating polar/cylindrical/spherical transformations, I've seen them vastly simplify operations that are otherwise hard to do the Cartesian way. :)
Aug
18
comment Why does the Mandelbrot set contain (slightly deformed) copies of itself?
All the fractal books go on about "fixed-point theory" and how the Mandelbrot set separates "attractive" from "repulsive" fixed points, as well as how it is related to the first self-similar object that was found in ancient times: the "equiangular (logarithmic) spiral". All this is a bit too dense for me. I for one would love to see a more accessible explanation to non-specialists.
Aug
18
comment $0/0$ limit question
Now that I think about it, changing the Cartesian variables in the original question to polar form also makes it clear that the limit does not exist: the role played here by $\theta$ is the same role played by m in your first answer.
Aug
18
comment An elementary way of simplifying a trigonometric triple integral?
Some elaboration would be welcome. :)
Aug
18
comment An elementary way of simplifying a trigonometric triple integral?
You sir, may be a day late, but a prince otherwise. :) Thank you! I suppose I owe you and other readers an explanation on the provenance of this triple integral so here goes: this appears as a coefficient in the series expansion of the "second virial coefficient" for the equation of state of a polar fluid. The integration over three angles represents the three degrees of freedom a polar molecule can move in a fluid. The triple integral appears in the book "Molecular Theory of Gases and Liquids" by Curtiss et al., but there is not even a hint that a simpler form for this exists.
Aug
18
awarded  Scholar
Aug
18
accepted An elementary way of simplifying a trigonometric triple integral?
Aug
18
comment Fitting a curve to a decreasing data set undefined at zero
On a less serious note, I think this thread has gotten an unprecedented number of comments...