19,857 reputation
24193
bio website sites.google.com/a/unca.edu/…
location Asheville, NC
age
visits member for 2 years, 7 months
seen 5 mins 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.


Aug
6
comment Using Solve but getting no output
You should be aware that there are many apparently simple equations with solutions that are not expressible in closed form. One such example is Solve[Cos[x]==x,x]. On the other hand, Solve[Cos[x]==x,x,Reals] produces a useful result. Thus, it's nice to now if your variables and parameters satisfy any useful assumptions. Lacking a symbolic expression, perhaps you'd be happy with a function that produces an estimate for s as a function of the input parameters?
Aug
6
comment How to generate specific function using BSpline command/
@chris I think it might be reasonable to implement PiecewiseExpand for InterpolatingFunctions but I don't see any reason to expect it. Interpolation is much older (V2) and lives in the numerical domain. PiecewiseExpand (V5) is primarily algebraic and is simply meant to simplify nested Piecewise expressions. How might PiecewiseExpand work with an InterpolatingFunction generated by NDSolve and containing zillions of sub-intervals?
Aug
5
comment How to draw a box with holes using Mathematica
@peter Honestly, I just looked at it. I figured the $z$ coordinate had to start way up high, go pretty low, then pretty high, then way down low - so I came up with $t-t^3$ over some interval. I then scaled and shifted that so that it fit. I did similar things with the $x$ and $y$ coordinates. Too much looking at functions over the years, I guess.
Aug
1
comment How to draw a box with holes using Mathematica
Are these really homotopic? Homeomorphic, I can see - but homotopic requires a deformation that disentangles those tubes. Given an explicit homotopy, we should be able to animate the deformation.
Aug
1
comment How to draw a box with holes using Mathematica
@peter You can learn a lot about this type of programming in the documentation's section on the structure of graphics. In particular, you'll learn that plotting command (like ParametricPlot3D) produce graphics primitives (like Line). So, if you execute something like InputForm[ParametricPlot3D[{t,t,t}, {t,0,1}], you'll see that a Line has been produced. The /.Line[pts_] :> business simply replaces it with a Tube.
Aug
1
comment Numerically solving Helmholtz equation in 2D for arbitrary shapes
@Mr.Wizard Not if I delete my answer! I am rather embarrassed to have the accept. :)
Jul
31
comment Numerically solving Helmholtz equation in 2D for arbitrary shapes
Why k=1/10? In fact, it seems that you can suppress the k entirely as t is playing the role of the parameter.
Jul
31
comment Numerically solving Helmholtz equation in 2D for arbitrary shapes
If you set numEigenToCompute=6 and then plot -efIF[[6]], you essentially get the MATLink Logo, though that was computed using a finite difference technique applied to a regular triangular grid.
Jul
31
comment Numerically solving Helmholtz equation in 2D for arbitrary shapes
I'm ridiculously excited!
Jul
24
comment Conversion of 3D plot to 2D Contour Plot
@user85503 thing[[position]] represents part extraction. If you execute Short[InputForm[pic], 4], you'll see that, internally, pic has the form Graphics3D[GraphicsComplex[pts_,_],_]. Now, pic[[1]] grabs the GraphicsComplex (since it's the first argument of Graphics3D) and pic[[1,1]] grabs the first argument of the first argument, namely the points - which is exactly what we need.
Jul
24
comment How to solve an operator form of an integral equation by iteration method?
Artes is correct that it's nice to see code in the question. Not only does it show some effort on the part of the OP, but it also lends context to the question letting the person answering the question know the appropriate level to write their own code. As I did encourage Javad to ask a follow up to this question, I'll provide an answer soon.
Jul
24
comment How to solve an integral equation by iteration method?
No biggie - you'll probably be an expert one day!
Jul
23
comment How to solve an integral equation by iteration method?
Please don't roll back my roll back! Honestly, it makes no sense for two reasons. Your original question refers to quite a specific operator so changing the operator wastes the efforts of those who answered the question. Secondly, this question has been closed so no one can answer it now anyway. If you have another question, simply open a new question.
Jul
23
comment Cellular Automata Neighborhood as Node connections
@Schwarz The Mod[Total[Table[value[gen - 1, v], {v, adjacentVertices[u]}]], 2, 1] business sets the new value to either 1 or 2, depending on whether the sum of the adjacent nodes is even or odd.
Jul
23
comment How to solve an integral equation by iteration method?
I've rolled back your question to it's original version, as I think your change of dimension is significant enough to warrant a new question. Feel free to open such a new question! Furthermore, no one can really answer this one, as it's closed anyway! (Not that I agree with the closure.)
Jul
23
comment How to solve an integral equation by iteration method?
@JavadKazemi I think the same basic idea should work, though it would be nice to have a specific example in mind.
Jul
22
comment How to solve an integral equation by iteration method?
I win - by 10 seconds! :)
Jul
22
comment HoldForm doesn't hold form
@MikeHoneychurch I've updated my answer to address the first example as well.
Jul
22
comment HoldForm doesn't hold form
I agree that you should consider contacting support. I'm not convinced that this is not by design, however. I've always found ThisForm[ThatForm[expr]] to be a bit awkward.
Jul
22
comment HoldForm doesn't hold form
@Jens Does the edit help? I guess that you've got to selectively apply Inactive to Set but not to InputForm. So Inactivate is a bit too coarse.