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5h
revised Solution for this question (Precalc)
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1d
comment Use the persistence theory to find a set of sufficient conditions for two species competitive ODE system
Sufficient for what...?
1d
answered An example of non euclidean inner product
2d
revised Theory of 4 colors
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2d
comment How can I integrate $\sqrt{1-x^2/a^2-y^2/b^2} dx dy$ in the ellipse?
Let $u=x/a$ and $v=y/b$, then change to polar coordinates.
2d
revised Is CHESS a-game of courtroom interest or conflict technique?
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2d
comment Idea behind Lyapunov functions?
Did you try reading the proof of Lyapunov's theorem somewhere? (That should answer your question, since the proof is precisely what explains how the conclusions follow from the hypotheses.) If so, was there anything particular that you got stuck on? As it stands, this question is rather vague and difficult to answer...
2d
comment What it means for a Jacobian determinant to be zero in the context of PDEs and their solution?
What book? Solution of which equation? There's not enough context in this question.
Apr
23
comment Interval arithmetic - faster version
You're welcome! (Note that in interval computations it might be more common to use closed intervals $[a,b]$ where the endpoints are included: $a \le x \le b$. And the two sign cases should perhaps be nonnegative/negative rather than positive/negative, so that you also take into account that one or both of the endpoints can be zero.)
Apr
23
comment Interval arithmetic - faster version
An interval $(a,b)$ is a set of the form $a < x < b$, so you need to have $a<b$ to begin with. (When you say "lowerbound" and "higherbound" you really mean the left and right endpoints of the interval on the number line, right?) Since $-1$ lies to the right of $-3$ on the line, it's not meaningful to talk about the interval "$(-1,-3)$".
Apr
23
comment A fun problem by Arnold using the Poincaré recurrence theorem
@MarcvanLeeuwen: Agreed, it would be better to refer to Weyl's equidistibution theorem. (As is implicitly done in Christian Blatter's answer.)
Apr
23
comment Flourish in functions
Hint: It's actually very easy to visualize this function; picture a horizontal line... ;-)
Apr
23
answered Interval arithmetic - faster version
Apr
22
comment How to solve this differential equation, involving leibniz notation?
Not confusing to me. ;-)
Apr
22
comment How to solve this differential equation, involving leibniz notation?
Actually one should be a bit more careful with absolute value signs for this to be a complete solution. (What about the case $y<-2$?)
Apr
22
comment How to solve this differential equation, involving leibniz notation?
How about setting $z(x)=y(x)+2$? Then you get $dz/dx=z$, which is a differential equation that I hope you can solve. ("Which function $z(x)$ equals its own derivative?") Or use the method of integrating factor. Or use the the characteristic polynomial ("homogeneous + particular solution"). Or use separation of variables (as already suggested in the answers). Etc.
Apr
22
comment Rational parametrization of circle in Wikipedia
What values of $t$ did you use then? Don't forget to include negative $t$ as well.
Apr
22
answered Example of a domain where all irreducibles are primes and that is not a GCD domain
Apr
21
revised Laplace's equation in Polar coordinate, an example?
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Apr
21
revised What is he easiest way to approximate γ as a decimal number?
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