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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.


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 $f(x) < 0 \forall x$
added 1 character in body
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
Jul
10
revised Need help with the graph of a function
deleted 1 character in body
Jul
10
comment Bessel's Equation
Yes, I'm sure that your textbook refers to your differential equation as Bessel's Equation. I'm saying that there is a special function, called Bessel's Function, which solves Bessel's Equation. The link I provided explains this in detail.
Jul
10
comment Bessel's Equation
Using a Bessel function, perhaps?
Jul
10
answered Need help with the graph of a function
Jul
2
comment Lecture notes ready for $\LaTeX$
@DaveL.Renfro If your looking for TeX documents, you can use the filetype modifier in your Google search, for example: fractal filetype:tex.
Jul
2
revised a system of finite difference equations
added 11 characters in body; edited tags
Jul
2
comment a system of finite difference equations
What do you mean by "solve" exactly? Clearly, $x_t=y_t=0$ for all $t$ is a stable equilibrium for the system and I'm sure there's at least one more equilibrium, which might or might not be stable. Do you mean more than this?
Jul
1
comment Calculate the length of curve
@Sacheo You're welcome, though I wouldn't be so fast to accept this answer - I think it's missing something and someone else may spot it.. You can always upvote without accepting.
Jul
1
revised Calculate the length of curve
added 251 characters in body
Jul
1
answered Calculate the length of curve
Jul
1
answered Plotting the inverse of a function
Jul
1
answered Reduced Residue System in Mathematica