Any book the elucidates the use of diffirentials?

[ronaldor9]

The trouble I have in reading mechanic books, at least the ones I have, is that they manipulate diffirentials as though they are algebraic symbols. Now, I know that typically the first year calculus student is told that the differential operator is to be viewed as one symbol and not the quotient of two diffirentials. Are there any books that can elucidate, and justify, the manipulation of diffirentials in such a manner without being too bogged down in rigor; or would I have to wait to study differential manifolds which I presume does place rigor in such manipulations?

 

[Daverz]

Here you go:

http://www.math.wisc.edu/~keisler/calc.html