[tptacek]

Yes! Separation of variables the other instance in the back of my mind. I suck at math (I've had basic ODEs for just a couple months now) but are there more examples like this?

I find this whole topic very gratifying because Leibniz notation seems very arbitrary and I'm glad it's not just me. :)

[leephillips]

More examples? Any undergraduate text in thermodynamics. The entire way the subject is taught depends on treating differentials as numbers. Even in partial derivatives.