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

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To solve a problem without fully understanding the underlying principles, one can rely on established mathematical frameworks, such as Gauss's Theorem of Divergence, even without a complete background in tensor calculus. It is acceptable to use formulas as long as they are applicable to the specific problem and sound reasoning supports their use. The discussion emphasizes that deriving complex formulas isn't always necessary, as long as the mathematical model accurately represents the physical scenario. Engaging with existing literature and seeking guidance from experts can also facilitate understanding without formal coursework. Ultimately, a balance between applying known formulas and developing a conceptual grasp of the problem is essential for effective problem-solving.
terryphi
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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.
 
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terryphi said:
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.
 

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