Recent content by chy1013m1

Homework Statement Given a set of sorted lists {X1, X2, ..., Xn} each Xi is in R^n , devise a divide and conquer algo that finds the median of X1\bigcup X2 \bigcup ... \bigcup Xn efficiently. (n * log(n), n^2 is not acceptable, also no probabilistic, expected runtime) Also, Xi \bigcap Xj =...

in one side of Stoke's theorem we compute curl(F ) . ndA . When we have computed curl(F ) in x-y-z coordinate, but have parametrized the surface in cylindrical / spherical coordinates, then in computing ndA, we do the cross product of the partials then times that by du dt (or somethin else) ...

Suppose F(x, y) is C1. F(0, 0) = 0. What conditions on F will guarantee that the equation F(F(x, y), y) = 0 can be solved for y as a C1 function of x near (0, 0) ? would it simply be dF/dy not equal 0 ?

so that means, if the Fretchet derivative is L, and the directional vector is u, it is just Lu.

Just to confirm, is the directional derivative of a vector valued function calculated as Lu ? where L is the Frechet derivative , and u is the unit vector in the direction. There seem to be a lot of sources for a real valued function's directional derivative, but very little on vector valued...

would all the points on the vector ab (a,b on the sphere) be on the sphere?.. i cannot see that and I don't think so.. I am just following the def of arc-connectness: A set S in Rn is arc-connected if any 2 points in S can be joined by a continuous curve in S, that is, if for any a, b, in S...

a sphere is convex? I know balls are convex.. just by intuition, a line from a -> b (a, b, on the sphere, the 'shell') is not on the shell of the sphere. .? since {(x, y, z) : x^2 + y^2 + z^2 = 1} , equality is required not <= (i may be wrong)

Homework Statement Show that the unit sphere {(x, y, z) : x^2 + y^2 + z^2 = 1} in R^3 is arcwise connected. Homework Equations The Attempt at a Solution find a continuous map f(t ) such that f( 0) = a, f(1 ) = b. a, b, in R^3 and are on the unit sphere. then show for every t in...

Homework Statement http://www.individual.utoronto.ca/chy1013m1/a42.jpg Homework Equations possibly Lagrange's multiplier..The Attempt at a Solution treating S = f(x1, x2, ... , x2006) = x1 * 1^1/3 + x2 * 2^1/3 + ... + x2006 * 2006^1/3 and constrain G(x1, x2 ... x2006) = x1 ^ 3/2 + x2 ^ 3/2 +...

so if I was to differenciate d(dZ/dx) / dx for F(x, y, z) = e^z + (x - z) * y - 4 = 0 i'd do: dz/dx = - (dF/dx) / (dF/dz) = - y * (e^z - y)^-1 then d (dz/dx) / dx = y * (e^z-y)^-2 * e^z * (dz/dx) is that correct ?

if z was solved in terms of x, y, then when we differenciate d (dz/dx) / dx, are we treating z as a constant or still a function of x, y ?

any insight to this question? .. i mean.. usually people just do up to order 2.. find the taylor polynomial of order 3 based at (x, y) = (0, 0) for the function f(x, y) = (e^(x-2y)) / (1 + x^2 - y) how large do you have to take k so that the kth order taylor polynomial f about (0, 0)...

just to check if i am on the right track.. let f(x ) = { e ^ (1 / (x ^ 2 - 1)) if -1 < x < 1 0 otherwise then it is easy to show that lim f( x) = 0 (split into 2 cases) x->1 or -1 it is also true that lim (f(x + h) - f(x)) / h = 0 for x = 1, -1 (show...

any thoughts to this question? Give an example of a C^oo (C infinity) function f : R->R which is positive on the interval (-1, 1) and 0 elsewhere