## Ghetto Mathematics post and replies

what's the deal?

desolderthis
2 Posts

Some things really test my faith in math
and physics.  Consider the following
example, use notation that ax/at means
partial of x wrt t. OK.  What is the
difference between this: a/ar[ a(phi)/ar ]
and this: 1/r^2 a/ar[ r^2 a(phi)/ar ] ?  If
you say nothing, then you are wrong.
Annoyed?  So am I.  The only difference is
one will give the right answer to a problem
and the other is garbage.

### Replies to what's the deal?

order matters -
Gary
Society of Physics...
293 Posts

I guess the first thing I would say is that you have to be careful about the order in which you do things...for example  d/dx(x^3) = 3x^2 and that is not the same as
x times d/dx(x^2) = 2x^2...

Adjunct Professor of Physics, Editor of The Physics Teacher, and GWU SPS Chapter Advisor

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Damian
Cypress
1 Posts

First off...you have to recall that phi(r).You have to use the chain rule to properly differentiate the second guy. The answer is 2/r*d(phi)/dr+d2(phi)/dr2. The first guy just gives you the second term of the second guy. phew...did that make sense? Be careful about spherical coordinates, there's a nasty singularity at the origin. For a rigorous discussion of this topic check out Electrodynamics by Griffin, an excellent upper div text on the subject.

Re: what's the deal? -

Dave
San Marcos, Texas
441 Posts

The difference is that in the second case, you are taking the partial derivative of a product, and so must use the product rule.  This gives you two terms instead of the single term that results from the first expression.

Dave

Try not to become a man of success, but rather try to become a man of value -- Albert Einstein

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