Hello, I did notice another thread that has a similar question but my question does not seem to fit perfectly into the OP's question so rather than hijack that thread I'll start a new one. I have found myself manipulating infintesimals algebraically. Recently I have read things that give me reason to believe this may be an incorrect thing to do that may or may not lead to correct results. For instance, say W = [tex]\int[/tex]F*ds = [tex]\int[/tex]mdv/dt*vdt I might simply say that dv/dt by dt is dv giving me = [tex]\int[/tex]mvdv But apparently this may not be a valid operation? I don't understand how it wouldn't be since, as I understand it, dv is simply a change in v (a number) that corresponds to a change in t of dt (dt being another number). From what I've found it seems "non-standard analysis" may give me insight as to what is going on here, but I do not want to spend time being side-tracked by this if it isn't worthwhile enough - perhaps my time would be better spent studying PDEs or fourier analysis. Especially if all non-standard analysis is going to give me is reassurance that what I'm doing is, in fact, a valid operation (I can take their word for it).