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  1. J

    Nonsingular derivative

    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?"
  2. J

    That given a continuous surface, contour lines exist

    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...
  3. J

    3x3 similar matrices defined by characteristic and minimal polynomials

    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)?
  4. J

    Cylindrically symmetric current distribution: Magnetic field in all space

    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...
  5. J

    Linear functional equivalence in vsp and subsp

    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...
  6. J

    Basis of a subspace of a vectorspace

    Is the basis for the subspace W of a vectorspace V spanned by the basis of the vectorspace V? If so how?
  7. J

    Interesting problem - movement of dialectric

    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?
  8. J

    NONUNIFORM Vol. Charge Density - V at the center of sphere

    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...