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visits member for 3 years
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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.


3h
revised Calculating Triple Integral
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3h
comment Calculating Triple Integral
@slmkarta Looks like you figured out the general idea while I was typing. My answer has some more details, but not all.
3h
answered Calculating Triple Integral
3h
revised How to visualize $f(x) = (-2)^x$
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5h
comment How did Sir Newton develop and formulate the famous binomial theorem?
To expand on Yves' comment, the basic binomial theorem for positive, integer powers is typically attributed to Pascal and Yves himself provides a nice answer for that. Newton generalized this to rational exponents. The easiest way to do so is to apply Taylor's theorem the function $(1+x)^p$, where $p\in\mathbb Q$ or even in $\mathbb R$. I'm not sure that this is how Newton approached the problem, though.
5h
comment Differential Equations and Newtons method
To answer your second equation, you first need the correct equation for $k$, namely $k^3+3k^2-1=0$ - i.e. exponents, rather than subscripts. You're asked to find the smallest positive root and then write down the solution. Your solution should look like $Ae^{1.23t}$, though $1.23$ isn't the correct number.
5h
comment Differential Equations and Newtons method
You've really got two fairly different questions so I would recommend that you ask separate questions on the site.
9h
answered How to visualize $f(x) = (-2)^x$
20h
comment Every projection of the square of the middle thirds Cantor set contains an interval
@Behaviour How can you tell, if the question is misstated? Here is a statement that definitely is true: If we project the point $(x_0,y_0)$ along a line of slope one, we hit the $x$-axis at the point $x_0-y_0$. Now, it's well known that $C-C=[-1,1]$; this can be proven using the triadic expansion representation of $C$. As a result, the projection along this direction certainly contains an interval.
1d
comment Proving that plane - cantor - set contains an interval
Something seems not quite right. The dimension of your set $C_{\lambda}$ is $\log(2)/\log(1/\lambda)$, provided that $\lambda<1/2$ - correct? If $\lambda\geq 1/2$, then $\dim(C_{\lambda})=1$. In any case, $\dim(E)=2\dim(C_{\lambda})$, not $\dim(C_{\lambda})$, as you have written. I'm guessing that your interesting situation is $1/4<\lambda<1/2$, where $E$ is a totally disconnected set with dimension greater than $1$.
1d
comment How many cube roots does 1 have modulo 162?
@MRK I didn't say that you need to upvote, I said you should simply because the answerer did put some effort into answering your question. Now, I don't tell my students to run straight to the computer for "every simple problem" (any more than I tell them to come here for such a problem), but I do tell them that it is often valuable to think about a problem from multiple perspectives - including computational.
1d
comment How many cube roots does 1 have modulo 162?
@MRK You needn't accept the answer but you should certainly upvote any answer that gives you a reasonable approach to think about the problem.
1d
answered Slightly Chunky Cantor Sets
1d
awarded  Yearling
2d
comment Why is it differential equations exist on an interval instead of a domain?
Because the domain happens to be an interval, according to the standard existence and uniqueness theorems.
Dec
11
revised Identifying Hamiltonian Systems with Phase Portrait
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Dec
10
revised Dynamical System , Series : can't find the general terms
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Dec
10
comment Dynamical System , Series : can't find the general terms
@Boo - The book is a classic!
Dec
10
answered Dynamical System , Series : can't find the general terms
Dec
9
revised Let there be 9 fixed point on the circumference of a circle.
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