21,394 reputation
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bio website sites.google.com/a/unca.edu/…
location Asheville, NC
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visits member for 2 years, 10 months
seen 9 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
9
awarded  Nice Answer
Sep
9
revised Mobius transformations revealed
added 402 characters in body
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
awarded  Self-Learner
Sep
9
answered Mobius transformations revealed
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
asked Mobius transformations revealed
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
9
revised Calculating a potential function using the finite element method
added 206 characters in body
Sep
9
revised Calculating a potential function using the finite element method
deleted 33 characters in body
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
5
awarded  Pundit
Sep
4
reviewed Reopen Eliminate z from two equations in x, y, z and plot y as a function of x
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
3
awarded  Enlightened
Sep
3
awarded  Nice Answer