1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Multivariable Calculus: Manifolds

  1. Aug 4, 2015 #1
    1. The problem statement, all variables and given/known data
    Let ##M## be the set of all points ##(x,y) \in \mathbb{R}^2## satisfying the equation

    ##xy^3 + \frac{x^4}{4} + \frac{y^4}{4} = 1 ##

    Prove that ##M## is a manifold. What is the dimension of ##M##?

    2. Relevant equations


    3. The attempt at a solution

    I think this question it started by saying the following:

    ##\phi=xy^3 + \frac{x^4}{4} + \frac{y^4}{4} - 1##

    Not overly sure how do this question so any help in the right direction would be appreciated. Anyway, I got the partial derivatives:

    ##\frac{{\partial}\phi}{{\partial}x}=y^3 + x^3##

    ##\frac{{\partial}\phi}{{\partial}y}=3xy^2 + y^3##

    After here I'm stuck, I can't find any clear way of answering this. Thanks in advance for any help.
     
  2. jcsd
  3. Aug 4, 2015 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    What is your definition of a manifold? Do you know the implicit function theorem?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Multivariable Calculus: Manifolds
  1. Multivariable Calculus (Replies: 1)

  2. Multivariable calculus (Replies: 1)

  3. Multivariable Calculus (Replies: 4)

  4. Multivariable Calculus (Replies: 1)

  5. Multivariable Calculus (Replies: 1)

Loading...