in_wolfram_we_trust

 Nov 26 comment Calculating the shortest distance between n number of points on a scatter graphHere's one counterexample on the real line. Our points are positioned at -1, 0, 1/2, 1, 2, 3, 4 ... 10. Starting at zero the naive algorithm moves to right then has to double back to hit the point at -1 for a total distance of 21. Nov 26 comment adjoint of a differential equationen.wikipedia.org/wiki/… Nov 26 comment What does it mean that solution of DE has ''n zeros''?A zero of a solution $f(t)$ is a point $t^{*}$ such that $f(t^{*}) = 0$. Nov 20 answered Differential operators confussion Nov 20 revised Differential operators confussionCorrected derivatives Nov 20 answered How to prove this ODE system is stable at origin? Nov 13 comment Pigeonhole Principle Question - Group of 6 people, do 3 either know each other or not?If there are 4 strangers and 2 friends, then certainly there are at least 3 people (3 of the strangers) that don't know each other. Nov 13 comment double integral to find volume of torusOkay - have a look at the partial answer I've posted below and try to finish the problem. I'll post some additional details once you tell me where you're getting stuck. Nov 13 revised double integral to find volume of torusdeleted 53 characters in body Nov 12 answered double integral to find volume of torus Nov 12 comment double integral to find volume of torusIf this is homework, please add the homework tag. If it's not homework, why do you need to integrate using Cartesian coordinates as well? Cylindrical is much easier and more appropriate for this problem. Nov 12 answered How do I find the middle(1/2), 1/3, 1/4, etc, of a line? Nov 8 comment Question on Riemann sumsI think your ideas are mostly right, but there are problems with some of your intermediate steps where you are missing absolute value signs around $f'$. Also, the final integral is missing a $\textrm{d}x$. Nov 6 answered Swapping differentials (rigorously) Nov 5 comment Divergence differential geometryWhat have you tried and where exactly did you get stuck? Do you know the definition of divergence as $\star\textrm{d}(\star F^{\flat})$? Are you comfortable working with the Hodge star operator? Nov 5 comment Inverse of Sum of Matrix InversesMinor point - surely it requires $N-1$ inversions to compute $\Gamma_{N}$? You get $\Gamma_{1}$ for free then need one inversion for each of $\Gamma_{2}$ to $\Gamma_{n}$. (I really wanted to add something more useful, but I couldn't think of anything after thinking about it for half an hour. I'm interested to see if there is a better way of doing it.) Nov 4 comment Script for the sum of the $j$-th powers of the first $n$ numbers in MATLAB@Edward I'm pretty sure Adriano's solution should work. What does sum([1:4].^2) give you? Nov 4 answered Rules for Product and Summation Notation Oct 31 awarded Good Question Oct 30 comment Explanation and Proof of the fourth order Runge-Kutta methodThe ODE has the derivative $dx/dt$ so we integrate on both sides with respect to time. On the right-hand side I'm using the dummy variable $\tau$ instead of $t$ since I want to use $t$ for the limits of integration.