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!

Totaly lost

  1. Nov 20, 2008 #1
    missed a lecture and now have this homework problem and dont even know what the upside down triangle symbol indicates, can someone please give me a hand getting started, thanks

    consider the vector function q=(1/4X^4 y^2 z, x^3 yz^6 - cosh(xz), 1/7x^3 z^7)

    calculate f(x,y,z)=upside down triangle . q
  2. jcsd
  3. Nov 20, 2008 #2

    D H

    Staff: Mentor

    That upside down triangle is the nabla symbol and is typically called "del". "Del" is an operator analagous to the derivative operator d/dx except that del takes partial derivatives. In Cartesian 3-space,

    [tex]\boldsymbol{\nabla} \equiv
    \hat{\boldsymbol x} \frac{\partial}{\partial x} +
    \hat{\boldsymbol y} \frac{\partial}{\partial y} +
    \hat{\boldsymbol z} \frac{\partial}{\partial z}

    When applied to a scalar function f(x,y,z), the del operator yields the gradient of the function:

    [tex]\boldsymbol{\nabla} f(x,y,z) \equiv
    \hat{\boldsymbol x} \frac{\partial f(x,y,z)}{\partial x} +
    \hat{\boldsymbol y} \frac{\partial f(x,y,z)}{\partial y} +
    \hat{\boldsymbol z} \frac{\partial f(x,y,z)}{\partial z}

    The operator definition of del looks like a vector. With a little abuse of notation, it can be applied to vector functions as a dot product (yielding a scalar) and a cross product (yielding a vector):

    [tex]\boldsymbol{\nabla} \cdot \boldsymbol{f}(x,y,z) \equiv
    \hat{\boldsymbol x} \frac{\partial f_x(x,y,z)}{\partial x} +
    \hat{\boldsymbol y} \frac{\partial f_y(x,y,z)}{\partial y} +
    \hat{\boldsymbol z} \frac{\partial f_z(x,y,z)}{\partial z}

    and similarly for the cross product. The expression [itex]\boldsymbol{\nabla} \cdot \boldsymbol{f}(x,y,z)[/itex] is called the divergence of f(x,y,z) while [itex]\boldsymbol{\nabla} \times \boldsymbol{f}(x,y,z)[/itex] is called the curl.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Totaly lost
  1. Lost on an Integral (Replies: 3)