Results 1 to 2 of 2

Math Help - Three Dimensional Transformation (Help Needed ASAP Please)

  1. #1
    Junior Member
    Joined
    Aug 2012
    From
    England
    Posts
    27

    Three Dimensional Transformation (Help Needed ASAP Please)

    I have been given the following problem and a unsure if I have established the correct answer or not? See attachment

    Thank You in advance for any help
    Attached Thumbnails Attached Thumbnails Three Dimensional Transformation (Help Needed ASAP Please)-revision-6.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Aug 2012
    From
    Oxford, UK
    Posts
    36
    Thanks
    2

    Re: Three Dimensional Transformation (Help Needed ASAP Please)

    I think the problem is asking you to choose a particular alpha and beta, and show that the expression on the left equals the Kronecker delta. Recall,

     {\delta^{\alpha}}_{\beta} = \left\{ \begin{array}{cc} 1, & \mbox{ if } \alpha = \beta \\ 0, & \mbox{ if } \alpha \neq \beta \end{array} \right.

    Let's do the example  \alpha = \beta = r , where  r = \sqrt{x^2 + y^2 + z^2}

     \frac{\partial z^{\alpha}}{\partial x^{\mu}} \frac{\partial x^{\mu}}{\partial z^{\beta}} = \frac{\partial r}{\partial x} \frac{\partial x}{\partial r} + \frac{\partial r}{\partial y} \frac{\partial y}{\partial r} + \frac{\partial r}{\partial z} \frac{\partial z}{\partial r}

     = \frac{x \sin{\theta} \cos{\phi}}{\sqrt{x^2 + y^2 + z^2}} + \frac{y \sin{\theta} \sin{\phi}}{\sqrt{x^2 + y^2 + z^2}} + \frac{z \cos{\theta}}{\sqrt{x^2 + y^2 + z^2}}

     = \frac{x^2 + y^2 + z^2}{r^2}

     = 1

    See if you can do it for other choices of alpha and beta.
    Last edited by JohnDMalcolm; August 12th 2012 at 07:30 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Transformation between two non-aligned 2-dimensional spaces
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: November 25th 2010, 09:30 AM
  2. Another trig help needed asap!
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 10th 2008, 07:33 PM
  3. HELP NEEDED PLEASE ASAP
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 8th 2008, 02:25 PM
  4. STATS Help Needed ASAP
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 21st 2008, 11:45 PM
  5. Surds Help needed ASAP
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 4th 2008, 05:37 PM

Search Tags


/mathhelpforum @mathhelpforum