a certain town never has two sunny days in a row. each day is classified as bveing either: sunny, cloudy (but dry), and rainy
if it is sunny one day, it is equally likely to be either cloudy or rainy the next day
if it is rainy or cloudy one day, then there is one chance in two that it will be the same the next day; if it changes, it is equally like to change to either of the two remaining possibilities
then the question asks about long run probabilities which we didnt do in class so Im sure it wont be on the exam, im not even sure he meant to do it as homework
@Semiclassic: A journal sent me an article to referee on using differential geometry to figure out the normal derivative of the electrostatic potential. They didn't buy my excuse that I'm retired ... or that it looked like stuff already in a book.
I mean, I remember one of the problems in the first chapter literally being to relate the principal curvatures at a point on a conductor to the field at the surface.
Right, but he's doing it in terms of principal curvatures of surfaces. It's still like stuff that's standard for understanding why soap bubbles are surfaces of constant mean curvature. But I guess I'll read it slightly carefully.
He references Jackson and says he does it "by an application of Gauss's theorem."
this is the part he didnt do cover in class, and that he has on the homework due tomorrow:
"What fraction of vehicles on the road are trucks? (set this up as a markov chain and computer the stationary distribution, whose components are the long run proprtion of time spent in each state)"
@TedShifrin Oui j'ai eu les oraux des Mines-Ponts lundi et mardi, et j'ai Polytechnique la semaine prochaine, les ENS celle d'après et Centrale en dernier si j'y vais
@TedShifrin I learnt a lot of fun math from the good crew (Astyx, Akiva, Daminark, Fargle etc) here. In theory, a bit about foliations but right now I have, as a project of the week, learning homotopy theory using the Moore method.
Yeah I figured I should finally learn them. I was recently a little a bit stressed (it's less than depression, really :P) so I figured it's a good side project for distraction.
Setting aside units, $\vec{D}$ is the electric flux density due to free charges, and $\vec{P}$ is the material's response to that electric flux. Then $\vec{E}$ is the combination of these two effects.
A flag on a bus is fluttering in north direction and wind is blowing in east direction. Then how do I determine the direction of the bus (using vectors)?
@Abcd: You want to add a vector pointing east and the velocity vector of the bus and get a vector pointing north. Draw a picture and see how that could happen.
A stationary probability vector $\pmb \pi$ is defined as a distribution, written as a row vector, that does not change under application of the transition matrix
fml, my book says "vector" to mean row vector
every book ive had so far, and Khan Academy, all assume "column" when saying vector
@Krijn Well my last year's English project was basically a sampling of a bunch of lines/paragraphs from whatever works of literature or poetry that came to mind, combined with a bunch of nonsensical and horrid stream of consciousness.
