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visits member for 4 years
seen Jun 24 '13 at 0:06

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
24
answered Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?
Aug
24
comment Derivative of a product and derivative of quotient of functions theorem: I don't understand its proof
The "logarithmic derivative" form is also useful when reckoning how uncertainties in data might propagate.
Aug
24
comment Infinite limits
IVlad: Whenever you get a result of ∞ (resp. -∞) from a limit calculation, simply consider it to mean that no matter how close you take your independent variable to the value of interest, you will never manage to find an upper bound (resp. lower bound). But there is still the issue of making sure both the left and right hand limits are consistent: one can probably say that the limit of xֿ² as x→0 is ∞, but the limit of xֿ¹ as x→0 does not exist in any sense of the word.
Aug
24
comment Proof that Pi is constant (the same for all circles), without using limits
Chris: that can be shown to be equivalent to "slicing up" the circle to form a "parallelogram" of appropriate dimensions; unfortunately for you this too involves limits.
Aug
24
comment Proof that Pi is constant (the same for all circles), without using limits
Sounds hard; its being transcendental seems to preclude the existence of a proof that won't appeal to the concept of limits.
Aug
24
comment Determine speed of the object at the current time by the non-uniform time sample
Well, using the monomial basis implies having to manipulate a Vandermonde matrix (no matter what norm you're minimizing in), and this can be ill-conditioned depending on point order and distribution. One could instead choose to use a Bernstein or orthogonal basis, and the matrix from these basis sets stands a better chance of being well-conditioned since the basis functions "don't look very much alike". Of course, if sticking with the rule of thumb I gave in a comment earlier, worries of ill-conditioning are probably moot and academic.
Aug
24
comment What is the best way to solve an equation involving multiple absolute values?
When you put it that way, then I certainly agree.
Aug
24
comment Do complex numbers really exist?
I liked the way an old electrical engineering book put it: "there's nothing imaginary about an electrical shock from j500 V!"
Aug
24
comment Determine speed of the object at the current time by the non-uniform time sample
...though, if pursuing the polynomial fitting approach, one can almost always do better than the monomial basis.
Aug
24
comment Determine speed of the object at the current time by the non-uniform time sample
Yes, I really do wish there was a functional form given to work with...
Aug
24
comment What is the best way to solve an equation involving multiple absolute values?
...so that's why your name was familiar! :D Macsyma really was a gem. Making a student algorithmically go through the steps of CAD for this still seems like "cruel and unusual punishment" to me though.
Aug
24
comment How do you define functions for non-mathematicians?
"the almost-never-taught intercept-intercept form" - I don't know why either, it's actually quite useful! It is also easily manipulated to a polar-coordinate form.
Aug
24
comment Determine speed of the object at the current time by the non-uniform time sample
...and examples like the Runge phenomenon inspire the oft-quoted rule of thumb that anything higher than a quartic fit to error-contaminated data might not be a good idea.
Aug
24
answered Determine speed of the object at the current time by the non-uniform time sample
Aug
24
comment Determine speed of the object at the current time by the non-uniform time sample
LP would be appropriate if you're fitting a polynomial to minimize with respect to either $\|\mathbf{x}\|_\infty$ (Chebyshev norm) or $\|\mathbf{x}\|_1$ (Manhattan norm); least squares would be fine most of the time, though. If the data exhibits non-polynomial behavior, however (e.g. asymptote-like behavior), then fitting globally to a single polynomial is poor form.
Aug
24
comment Showing $\frac{1}{x}-\left[\frac{1}{x}\right]$ is Riemann Integrable
I personally am not fond of using brackets for denoting the floor function... that's just me, though.
Aug
24
comment What is the best way to solve an equation involving multiple absolute values?
I knew somebody would invoke CAD at some point; this is in fact what Mathematica uses internally for such sets, FYI. On the other hand, I can't imagine making a student do CAD manually!
Aug
23
comment What is the best way to solve an equation involving multiple absolute values?
For someone who has to solve a lot of equations of this sort, I would always recommend that the first thing to do is to make a plot of the functions of interest, if only to reckon which intervals one should be looking at.
Aug
23
comment Find the coordinates in an isosceles triangle
Right. Sadly I cannot vote twice!
Aug
23
comment Find the coordinates in an isosceles triangle
Didn't want to waste the programming effort, 'no? ;)