10,673 reputation
1132
bio website sites.google.com/a/unca.edu/…
location
age
visits member for 3 years, 1 month
seen 16 mins ago

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.


15m
revised How to find the normal vector in a TNB problem
added 4 characters in body
35m
answered How to find the normal vector in a TNB problem
46m
revised How to find the normal vector in a TNB problem
added 131 characters in body; edited title
3h
comment Get a function (equation) from data points?
You might be interested in Michael Trott's blog post indicating how he automated the procedure to find a curve to mimic just about anything you want.
7h
comment Graphing algorithm
When you say that it's "hard to reduce to the form of $y=f(x)$", I guess you mean an equation like $x^3 - x y + y^4=0$ or some such? In other words, you're primarily interested in how to plot general equations, where one variable is a function of the other variable only implicitly. Correct?
10h
revised Diffusion equation problem
added 655 characters in body
12h
comment How was the explicit closed form for this implicit function derived?
@user1963 Honestly, I picked the one that led to the answer you wanted. :) I suspect that the other root is excluded by the assumptions $0\leq z+H(z) \leq 1$ and $-1\leq z-H(z) \leq 0$, but I didn't check.
14h
comment How was the explicit closed form for this implicit function derived?
@user1963 I don't believe so. The assumption in the previous paragraph is that $0<z+H(z)\leq1$ and, according to the piecewise definition of $F_z(arg)$, we should use the version of $F_z$ with the leading minus sign, when $0<arg\leq1$. Note that $arg$ here stands for "argument" and I'm trying to distinguish that argument from $z$; in this case, the argument is $z+H(z)$. Also, I solved the equation in Mathematica and it seemed to give the correct answer.
15h
revised Does $\sin(x+iy) = x+iy$ have infinitely many solutions?
deleted 593 characters in body
23h
revised Coming Up With A Neutral Fixed Points Theorem
added 2 characters in body
23h
comment Coming Up With A Neutral Fixed Points Theorem
@Uzman Conjugacy is described in several places in Devaney's text. Functions $f$ and $g$ are conjugate if there is a function $\phi$ such that $f(\phi(z))=\phi(g(z))$. This allows us to conclude that $f$ and $g$ have similar dynamics. When I say "local conjugacy" I mean that, $\phi$ maps a fixed point $z_0$ of $f$ to a fixed point $\phi(z_0)$ of $g$ but that the conjugacy is only good in a neighborhood of $z_0$.
23h
comment Coming Up With A Neutral Fixed Points Theorem
@Uzman We say that $f(x)=g(x)+O(h(x))$ if there is $C>0$ such that $|f(x)-g(x)|\leq C|h(x)|$. Typically, $h(x)$ is close to zero and we're saying that $f(x)$ is close to $g(x)$ and $h(x)$ is a measure of how close. In this context, $O(x^{n+1})$ for $x$ close to zero essentially says that we have terms of that order and higher that are negligible compared to the smaller order terms.
1d
answered Coming Up With A Neutral Fixed Points Theorem
1d
comment heat equation, total heat energy
I answered a very similar question earlier today. I hope that one helps!
1d
comment Determine a matrix knowing its eigenvalues and eigenvectors
@user3435407 Yep - I guess I don't get what you don't get. I added one check.
1d
revised Determine a matrix knowing its eigenvalues and eigenvectors
added 280 characters in body
1d
answered Determine a matrix knowing its eigenvalues and eigenvectors
1d
comment What will the graph of this parametric equation look like?
There are a number of online tools that you can use to explore this sort of thing, like WolframAlpha.
1d
revised Diffusion equation problem
added 753 characters in body
1d
comment Diffusion equation problem
@mikerussel Not quite. You're looking for a steady state function, so it shouldn't depend upon $t$. You might write just $u(x)$ or even $u(x,\infty)$. Given that change, though, yes - you're looking to express $u(x)$ in terms of $f$. The value of $u(x)$ will be constant, namely the average temperature in the bar, as in my answer.