Book recommendation on infinitesimals I'm a sophomore mechanical engineering student and I'm looking for a book which completely describes the concept of "infinitesimals"  (used in thermodynamics or dynamics or...), In fact, I was taught that dy/dx is not quotient ,but in physics it seems they are treated and being manipulated like numbers

Since differential geometry seems to be the flavour of this thread, my recommendations are as follows.
Personally, I think the best text for differential forms is set out in R.W.R. Darling's Differential Forms and Connections: see link here.
For a physics slant, try Nakahara's Geometry, Topology and Physics, the text can be found here.
Personally, when I was a mathematics undergraduate, I found John McCleary's Geometry from a Differentiable Viewpoint (here) and Differential Geometry by Kreyszig (here) indespensible but appreciate it may be more suited to a math Major.
