Advice Wanted:How To Solve A Problem Without Really Understanding It

[terryphi]

Hi,

I'm in a situation where I know the formula I need to solve a problem but I don't know how to derive it.

(I'm trying to derive a formula for an isotropic point source in a vacuum)

The correct solution requires the use of Gauss's Theorem of Divergence, but I've never taken a course on tensor calculus.

Although it's a bit unorthodox, I'd still like to ask:

How can I solve this problem 'properly' (IE not just plugging values into a formulae) without going through a whole course on tensor calculus?

Or more generally:

How does one solve a problem without having the background?

Thanks for any insight you might have.

 

[Cleonis]

How can I solve this problem 'properly' (IE not just plugging values into a formulae)

Maybe the following comparison is helpful. When a physicist uses differential calculas there is no obligation to derive differential calculus itself.

'Plugging values in a formula' is OK if that formula is in itself not specific to the problem at hand.

The obligation then is to give sound arguments that the mathematics of the particular formula you're using is a good model for the physics that you want to describe.