Solved

grad(dg/dr) dot grad r = d^2 g/dr^2

Posted on 2008-11-01
4
517 Views
Last Modified: 2010-05-18
I'm trying to get from (13) to (14), here:
http://mathworld.wolfram.com/Laplacian.html

I've managed to show that the first terms equate:

dg/dr div(grad r) = 2/r dg/dr,

but I'm struggling to equate the second terms:

grad(dg/dr) dot grad r = d^2 g/dr^2

Can anyone spell it out for me please?

Thank you.
0
Comment
Question by:InteractiveMind
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 2
4 Comments
 
LVL 27

Expert Comment

by:aburr
ID: 22858227
The rs are unit vectors.    I do not think your starting equation is
grad(dg/dr) dot grad r
0
 
LVL 25

Author Comment

by:InteractiveMind
ID: 22861982
The same equation can be derived if you assume that r is a function of (x,y,z) with r(x,y,z) = sqrt(x^2+y^2+z^2). In which case, grad r = (x,y,z)/||(x,y,z)||, which we can call r hat.
0
 
LVL 25

Accepted Solution

by:
InteractiveMind earned 0 total points
ID: 22867134
<grad(dg/dr), grad r>
= (Drr g Dx r, Drr g Dy r, Drr g Dz r) dot grad r
= Drr g <grad r, grad r>
= Drr g

As required.
0

Featured Post

Free Tool: Site Down Detector

Helpful to verify reports of your own downtime, or to double check a downed website you are trying to access.

One of a set of tools we are providing to everyone as a way of saying thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Relative Frequency Distribution 4 40
Probability Distribution 5 57
Random Variable 2 62
Math question 3 122
How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! https://www.google.com/about/careers/students/guide-to-technical-development.html How to Know You are Making a Difference at EE In August, 2013, one …
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

738 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question