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I received my Ph.D in mathematics from Ohio State in 1994 under the direction of Gerald Edgar and have been a professor of mathematics at The University of North Carolina - Asheville since 1997. In recent years, I've also worked as a part-time consultant to Wolfram Research focusing on development of mathematical content for WolframAlpha.


Aug
10
comment My first partial differential equation attempt
@Dmoreno I'm glad you liked it. I generate the image with Mathematica. I generated a list of images and then exported that to an animated GIF. The command to generate the list of images was something like so: Table[Plot[Exp[-Pi^2 t] Sin[Pi*x], {x, 0, 1}, PlotRange -> {0, 1}], {t, 0, 0.7, 0.01}].
Aug
7
revised Can the graph of $x^x$ have a real-valued plot below zero?
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Aug
6
reviewed Approve suggested edit on Get position of a point with known distance between other points
Aug
6
comment Get position of a point with known distance between other points
Well, there's a fairly obvious system of equations to write down. Do you have a specific example?
Aug
6
answered My first partial differential equation attempt
Aug
6
comment Non-Trivial Self-Inverse Analytic Function In The Complex Plane
This is a well studied problem on the Riemann sphere - namely the complex plane plus infinity. In that context, the only holomorphic, self-inverse functions are the Mobius functions, $z\rightarrow (az+b)/(cz+d)$. In the everywhere analytic case, $c\neq 0$ and you're left with your two examples.
Aug
6
comment Analytic Function In The Complex Plane Which Always Gives Real Values
You can use the Cauchy-Riemann equations to prove fairly easily that, if $f$ is defined and analytic for all $z$ in the complex plane, then $f'=0$ on the complex plane. It follows that $f$ must be constant.
Aug
6
comment Optimization Software
You need to ask a much more precise question. If you're using Mathematica, you might consider asking on mathematica.se but, again, you must reference a specific example. Is there any chance you're using the Minimize command command when NMinimize would be more appropriate?
Aug
2
comment interpreting triple integrals
You could make the question more clear with a specific example.
Aug
1
comment Limit of a Discrete Dynamical System
@user54738 Many software packages provide the ability to do numerical computations to much higher precision that just the 16 decimal digits provided by the CPU. I used Mathematica which provides significance tracking so that you can actually measure how precise your computations are. As a result, you can have confidence of your results. To see the need for this sort of thing, try iterating $f(x)=4x(1-x)$ from $x_0=(2+\sqrt{3})/4$ at machine precision. It will appear to converge to $0.75$ (correctly) but, after around 40 iterates, it moves away from $0.75$, even though $3/4$ is fixed.
Jul
31
revised Can you uniquely define a tangent line at a point for a 3D csurve?
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Jul
31
answered Can you uniquely define a tangent line at a point for a 3D csurve?
Jul
31
answered Limit of a Discrete Dynamical System
Jul
23
awarded  Revival
Jul
20
answered Triple Integral exercise
Jul
17
comment Prove $f(x) < 0 \forall x$
@Mr.T Please take a look at our FAQ on homework and pay particular attention to the part labeled "Why don't you provide a complete answer to my question?". Now I don't know for sure that this is a homework assignment but, even if it is not, it's clearly at that level and I wouldn't want to rob you of the joy of discovery. :) In that context, the response is appropriate. Incidentally, you should upvote all answers that provide at least some assistance, though you might choose to accept a later answer, if it is forthcoming.
Jul
17
revised Prove $f(x) < 0 \forall x$
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Jul
17
answered Prove $f(x) < 0 \forall x$
Jul
17
comment System of non-linear ODE's
By "analytically", you mean to find closed form expressions for $x(t)$ and $y(t)$? Mathematica is unable to find such expressions and I see no reason to think that such expressions exist. On the other hand, you can "analytically" find that the origin and $(p/3,p/12)$ are equilibria, use linear algebra to classify the behavior at those points, and finally see how these fit into the vector field determined by the system.
Jul
14
revised Need help with the graph of a function
deleted 27 characters in body