17,809 reputation
13687
bio website sites.google.com/a/unca.edu/…
location Asheville, NC
age
visits member for 2 years, 5 months
seen 8 hours ago

I've been a professor of mathematics at The University of North Carolina - Asheville since 1997. I've been using Mathematica since I started graduate school in mathematics at Ohio State in 1989. At that time, we used version 1.1 (as I recall) to teach calculus in our Calculus and Mathematica classes. I've used it pretty much continuously in my teaching and research since then.

In addition to my posts on SE, you can find some of my papers, teaching notebooks and other Mathematica based oddities strewn throughout my website.

In recent years, I've also worked as a part-time consultant to Wolfram Research focusing on development of mathematical content for WolframAlpha.


Feb
17
comment Is it possible to use WolframAlpha servers to evaluate equations in Mathematica v8.0.4?
And, perhaps, this will soon be of interest: online.wolfram.com
Feb
16
comment iterating piecewise linear maps on [0,1]
@ssch In this case, that's true. For other maps, the expression swell may be worse.
Feb
16
comment DensityPlot on spherical surface?
The key point in that other answer (that is relevant to your question) is that the textures work well on spheres, if you start with an image in the correct coordinate system. That point is not really "beyond" your question; I think it's exactly what you need.
Feb
16
comment DensityPlot on spherical surface?
If you have the data, then the basic idea outlined in this answer should be applicable: mathematica.stackexchange.com/questions/15047/…
Feb
16
answered iterating piecewise linear maps on [0,1]
Feb
16
comment Badly conditioned matrix (General::luc)
Numerical inversion of a matrix is both slow and poorly conditioned, a fact mentioned in most books on numerical analysis. Typically, a solution to an applied problem can be formulated in such a way that matrix inversion is expressed in terms of the solution of a system of equations. Naturally, it would be much easier to provide details if you provided more details of your problem.
Feb
16
comment iterating piecewise linear maps on [0,1]
@ssch I'd say that your dyadic is the natural translation of the Bernoulli shift on two symbols to the unit interval, yes.
Feb
13
revised Finding all points of period n in an iterated map
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Feb
13
revised Finding all points of period n in an iterated map
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Feb
12
answered Finding all points of period n in an iterated map
Feb
12
comment Finding all points of period n in an iterated map
Very nice! The technique in the paper requires that we find all orbits up to period on the order of 20 or even more. The NDSolve command chokes on that but should run with the option Method->{"EquationSimplification"->"Solve"}. Also, I suppose that your initval could be fiddled with to allow for the need to find more orbits.
Feb
7
reviewed Approve suggested edit on Using Outer with Compiled functions that accept more than 2 arguments
Feb
5
comment Calculating orbital period for the logistical map
@JackHenahan I don't think this approach will work for orbits of that length. Off hand, I can think of two possibilities. (1) You might be able to exploit the regularity of the period doubling cascade to locate $a$ and $x_0$ values that work. (2) Symbolic dynamics might be applicable. Sounds fun - wish I had time to think more about it. :)
Feb
5
comment Calculating orbital period for the logistical map
@JackHenahan As my latest edit shows, you don't need high precision to find reasonably long attractive orbits.
Feb
5
revised Calculating orbital period for the logistical map
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Feb
4
comment Calculating orbital period for the logistical map
@JackHenahan Given that there is a single attractive orbit, higher precision is really not particularly necessary here. Also, Mathematica's automatic error precision tracking tends to be overly pessimistic in this situation. It would make a lot more sense to use high precision numbers in a case like $a=4$. If you can modify your question to clearly indicate what you hope to accomplish using high precision numbers, I might be able to assist on that issue. (I didn't notice any mention of precision in your original post, other than the one instance of WorkingPrecision in the Mathematica code.)
Feb
3
answered Detect highest order of derivative in expression?
Jan
31
answered Calculating orbital period for the logistical map
Jan
30
revised How can I make the output from Solve look nice?
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Jan
29
revised How to check if an expression is a real-valued number
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