Recent content by Reb

  1. R

    Involving Landau's 'big oh' notation

    (don't have an answer yet) We say that two sequences f,g are f=O(g) if-f there is a c>0 such that |f(n)|<c|g(n)| uniformly as n tends to infinity. If g(n)>2, does f=O(g) imply lnf=O(ln(g))?
  2. R

    Other Should I Become a Mathematician?

    There's also a different side to doing math. Reading from S. Ulam's "Adventures of a Mathematician": "In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some...
  3. R

    What is the geometry of the pseudo sphere and what dimension does it exist in?

    Well, if I was to transform the question into the Euclidean setting, I would ask why would someone need to bother with what a plane is, in order to define straight lines! What I mean is that there is a minimum of insight required in order to go into the theory of geodesic distance, and this...
  4. R

    Is There a Limit to the Possible Metrics on a Riemannian Manifold?

    That's a bit funny to ask, since a Riemannian manifold must come along with a metric. Yes there is. That's what enables one to define the Levi-Civita connection in the first place. You can look it up in every good book about Differentiable Manifolds (like Do Carmo's book)...
  5. R

    What is the surface area of a Mobius strip made from a strip of paper?

    I'd be surprised. http://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/moebius.html" [Broken] page calculates for us that, for the standard parametrization,
  6. R

    Parabolic PDE in Curved Spaces: Exploring Solutions on Manifolds

    On a manifold, that is... I know http://www.cambridge.org/US/catalogue/catalogue.asp?isbn=9780521409971" [Broken] book that deal with qualitative properties of the solution of the heat equation on a manifold (which, since the Laplacian depends on the metric, becomes non-constant...
  7. R

    Lagrange Multipliers: Exploring G, f, and g

    Not really. Under the given conditions, the implicit function theorem guarantees that the expression f(p)=f(p_1,p_2)=0 defines a function y=y(x), x\in (p_1-\epsilon, p_1+\epsilon)=I (or x=x(y), but choose the former for convenience) . So an extremum for g on f^{-1}(0) is in fact the extremum of...
  8. R

    What is the surface area of a Mobius strip made from a strip of paper?

    Yeah, but they also don't. Anyway, I'm not a vector, I'm a human being (dammit). I'm not linear, and I'm surely not stable.
  9. R

    What is the solution to a 3rd order nonlinear ODE?

    How about ...you re right? I mistakingly assumed that every solution has to meet the y axis.
  10. R

    Solving Advanced ODEs: Help Needed!

    Ok let's see... For 1), you are given the ODE with the parameter shifted by a small \epsilon, and you are required to show that this new ODE with \epsilon will have an equilibrium, which is "close" to the original one. Since f_a has nonzero gradient, continuity implies that f'_{a+\epsilon}...
  11. R

    What is the solution to a 3rd order nonlinear ODE?

    Three constants? That would be the case if the ODE was linear. There is another problem here. The ODE is autonomous, and all functions of the form y=const. are solutions, plus the solutions cannot meet each other. So this ODE has only trivial solutions.
  12. R

    Integration/Differentiation on abstract spaces

    The http://en.wikipedia.org/wiki/G%C3%A2teaux_derivative" [Broken] derivative. Integration on Banach spaces is a more delicate subject. There is however an approach parallel to the construction of the Lebesque integral. A taste of it...
  13. R

    Equation of a Curve in R3 with Constant Inclination: Need Help!

    This is called a curve of 'constant inclination', as t/k=1=cotan(a), where a is a constant angle formed by the tangent to the curve and a specific fixed direction. This will make integration easier. Ps. There is (free) software on the internet, which will draw a curve on the input of...
  14. R

    Geodesic deviation & Jacobi Equation

    They are the same notion under a different name: The Euler-Lagrange equations for the variation of geodesic length, over the space of geodesics with fixed ends.
Back
Top