20,521 reputation
24498
bio website sites.google.com/a/unca.edu/…
location Asheville, NC
age
visits member for 2 years, 8 months
seen 4 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.


Sep
12
comment Strange behaviour of MMA in derivatives of some standard functions
The functions you explore are all non-analytic as complex functions, thus the derivative is undefined. You might explore the numerical derivative ND as defined the NumericalCalculus package.
Sep
11
comment Homotopy Visualization
I did something like here to illustrate graph isomorphism. That's much simpler, though, really. Shouldn't be to hard to grab a set of points describing the boundaries of the objects but it might be tricky to maintain the topological integrity throughout the animation.
Sep
11
comment Homotopy Visualization
I guess you mean a homotopy, actually.
Sep
10
comment How do I plot the images of oriented curves under complex transformation?
How about Show[r1, r1 /. Line[pts_] :> Arrow[pts, 2]]?
Sep
9
comment Calculating a potential function using the finite element method
@Hugh There certainly are other ways to make a mesh. In this answer I show how to interface with a free, third party program called triangle that might do what you want. However, I'd think that converting them to the ElementMesh format that you want would be rather involved. Also, V10.0.1 is due out any day and I'm quite certain that bugs in mesh generation have been addressed, though I'm not certain if this specific issue is improved or not. Will definitely be worth checking out, though.
Sep
9
comment Mobius transformations revealed
@YvesKlett Seems like a reasonable expectation. :) I do have an implementation based on simple graphics primitives that I'll post soon.
Sep
9
comment Calculating a potential function using the finite element method
@s.s.o I didn't notice the {0,0} issue - thanks!
Sep
9
comment Calculating a potential function using the finite element method
@s.s.o The value of MaxBoundaryCellMeasure is ignored in your code, which is why it alleviates the problem. Using ToElementMesh directly on reg allows one to at least reduce the value of MaxBoundaryCellMeasure somewhat before the problem starts.
Sep
9
comment Calculating a potential function using the finite element method
@Hugh Essentially, that's correct. Technically, though, it's interpolating, rather than extrapolating. :)
Sep
9
comment Calculating a potential function using the finite element method
The return value of NDSolveValue is an InterpolatingFunction, which describes how to compute values between points on the grid. That answers your question 4 and also indicates what's going on in question 5 - namely the interpolation order is too low to expect to do better. Unfortunately, I don't think it's so easy to increase that on an unstructured grid. Also, I'm not so sure how well MaxBoundaryCellMeasure works and your problem with the mes on the circle seems to be alleviated when you delete it. That option isn't even available to DiscretizeRegion.
Sep
8
comment Should eigenvalues be ordered?
So, what do you think of the output of this: Sort[{1, 2, 4, Sqrt[Pi]}]? I think it's reasonable in a symbolic system.
Sep
8
comment How can Mathematica help me to find a real radical expression for roots of this polynomial?‎
See Casus Irreducibilis and/or this notebook. The roots can be expressed without the imaginary unit, if you are willing to accept trig functions - just hit your output with ComplexExpand.
Sep
7
comment NSolve transcendental equations
There are infinitely many solutions. You can find quite a few of them like so: Chop@NSolve[Abs[al] < 2 && Abs[R] < 2 &&Cos[al] == R/(0.0496045 + R) && Cos[al + 0.1/R] == R/(0.05 + R), {al, R}]
Sep
3
comment How to speed up my Project Euler code
If you realize that the maximum solution is 10 Floor[Ceiling[Sqrt[1929394959697989990]]/10] and step down by 10 from there, you'll get the solution almost immediately.
Sep
2
comment How to Nest a Function with three Arguments?
I suspect he'd like it to work with arguments other than A, B, and dt. Perhaps, a more general pattern would be appropriate?
Sep
2
comment How to prove that all zeros of the complex polynomial $P(z)$ lie in the closed unit disk $|z| \leqslant 1$?
Wrong site - I suspect you want math.stackexchange.com
Sep
2
comment How to find this limit correctly?
I suppose that Assumptions in Limit might simply be applied to simplify the expression ahead of the computation. That would explain the difference in the results and be dismissed as designed. A genuine domain restriction would be more properly dealt with as a third argument.
Sep
2
comment How to find this limit correctly?
@DanielLichtblau That is what I thought. But, then, how do I explain the fact that Limit[n^2 Sin[2*n*Pi], n->Infinity, Assumptions->Element[n, Integers]]==0?
Sep
1
comment How to find this limit correctly?
@belisarius Well, yeah, but that's a discrete plot indicating the limit is $2\pi$ ( I assume, I'm on my iPhone).
Sep
1
comment Importing High Precision (22 digits) data from a file
@jason There is no import as string in my example. I used ImportString since it works exactly as Import but allows one to show a whole example without reference to an internal file. If you want that specific number, then that specific number will need one more zero in your input file. Keep in mind also that you should get the binary number with the specified precision closest to your input, so that trailing digits are often present. I can't verify your 8.24574098106 as I get 8.24574097909*^8, which seems quite right.