What does a "nonsingular derivative" mean. It comes in the following context: "If f: R^2 --> R^2 is a function with a nonsingular derivative everywhere, is f bijective?"
Can you guys help me prove: Given a continuous and differentiable function (or surface) f: R^2 -> R, such that f(x,y) = z ... contour lines can always be drawn... the function is NOT bijective.
I've been thinking of choosing any arbitrary point and showing that the curves that intersect to...
Why do you guys think that given two 3x3 matrices, they are similar if and only if their characteristic polynomial and minimal polynomial are equal (this reasonably fails for 4v4 matrices though)?
Homework Statement
a. An infinite cyclindrically symmetric current distribution has the form
\vec J (r, \phi, z) = J_0 r^2/R^2 \ \ \ \vec\hat \phi for R<r<2R. Outside the interval, the current is 0. What is the field everywhere in space?
b. An infinite cyclindrically symmetric current...
I am writing a solution for the following problem, I hope someone can correct it, because I am not sure what I am missing.
Q. V is a finite dim. vsp over K, and W is a subspace of V. Let f be a linear functional on W. Show that there exists a linear functional g on V s. t. g(w)=f(w).
Ans...
This is a problem was thinking about.
If I have a capacitor and fill it with a dialectric of some dialectric constant (the dialectric fits perfectly and is mounted via a frictionless bearing so it can move freely). How fast does it move?
This should be easy, but for some odd reason I am not getting the right answer.
Assuming the potential V=0 at infinity, what is the V at the center of a sphere with volume charge density rho(r) = rho_0 * R/r
I keep getting (integral from 0 to R K*(4*pi*rho_0)*R/2) which I dont think is...