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Vector Calculus question

  1. Mar 24, 2009 #1


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    My vector calculus is a bit rusty. Can anyone tell me if the following uses proper symbolism?

    F &= \left[\begin{matrix}f_1(x_1,x_2) \\ f_2(x_1,x_2) \\ f_3(x_1,x_2) \end{matrix}\right]
    \qquad x = \left[\begin{matrix} x_1 \\ x_2 \end{matrix}\right]
    \qquad \frac{DF}{dx}&=
    \rule{0pt}{3ex}\frac{\partial f_1}{\partial x_1} & \frac{\partial f_1}{\partial x_2} \\
    \rule{0pt}{3ex}\frac{\partial f_2}{\partial x_1} & \frac{\partial f_2}{\partial x_2} \\
    \rule{0pt}{3ex}\frac{\partial f_3}{\partial x_1} & \frac{\partial f_3}{\partial x_2}\end{matrix}\right]
    Last edited: Mar 24, 2009
  2. jcsd
  3. Mar 24, 2009 #2
    The first two look correct, but I don't think [tex]\frac{DF}{dx}[/tex] is a common notation. I would use just [tex]DF[/tex] or maybe [tex]\frac{\partial f}{\partial x}[/tex].

    Edit: http://en.wikipedia.org/wiki/Jacobian_matrix" [Broken] uses the notation [tex]J_F[/tex].
    Last edited by a moderator: May 4, 2017
  4. Mar 31, 2009 #3
    Im very turned around in vector calc! I have the equation 4y2 -4z2=5y/x-4x2 and I need to convert it from rectangular to cylindrical coordinates. Could someone explain this better than my professor?
  5. Mar 31, 2009 #4
    Hi, Jon89bon!

    I had a bit of vector calculus in my first semester at the university and I'm not sure if what I paste here is truely correct, so it would need an overview from a supervisor :)

    Here's what we do:

    1. we transform the equation: 4y^2 -4z^2=5y/x-4x^2 into

    (4y^2 -4z^2+4x^2)x-5y=0=:f(x,y,z) and set a func. f equal to it.

    2. As f is a SCALAR field, we could use the transformations:

    (x,y,z)=(rcos(a),rsin(a),z), where r^2=x^2+y^2 and a is the angle of rotation around the z-axis

    remark: if you're good at algebra, you could skip the first step :)

    IMPORTANT: I think, this transformation does not apply to vector fields (when f is a vector), but I need an approval for that statement from s.o. else :)

    all the best, marin
    Last edited: Mar 31, 2009
  6. Mar 31, 2009 #5
    Thanks I will work with this and see what I come up with!

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