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!

Vector analysis

  1. May 24, 2014 #1
    1. The problem statement, all variables and given/known data

    This picture is taken from Div, curl, grad and all that by schey, while finding the unit normal vector of the surface S (defined as w=f(x,y)) at a point P, to find the normal vector he considered a two tangent non-collinear vectors (u and v) at a point P, to find u he considered a plane passing through point P parallel to xz plane, the plane which intersects the surface S traces a curve C which contains the point P, he drawn a tangent to the curve at the point p, let the x component be ux, My question is how the z-component of u is (∂f/∂x)ux ?

    2. Relevant equations
    No equations found


    3. The attempt at a solution
    I have an idea that z-component of u is some approximation, but i havn't learn multivariable calculas a lot, so please enlighten me. Thank you
     

    Attached Files:

  2. jcsd
  3. May 24, 2014 #2

    CAF123

    User Avatar
    Gold Member

    You are correct. In a small displacement from P, the linear approximation is a good one and you can write ##z(x= P + u_x) \approx z(x=P) + \frac{\partial z}{\partial x} u_x## (The Taylor expansion truncated, ignoring higher order terms). For an infintesimal displacement, this approximation becomes exact.
     
    Last edited: May 24, 2014
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: Vector analysis
  1. Vector analysis. (Replies: 3)

  2. Vector analysis (Replies: 9)

  3. Vector Analysis (Replies: 1)

  4. Vector analysis (Replies: 5)

  5. Vector analysis (Replies: 2)

Loading...