Anyone who sees calculus in application is likely to encounter both derivatives and differentials. The two concepts have confusingly similar notation. For that reason, this post is a very important contribution.

Jul 13, 2015 · The right question is not "What is a differential?" but "How do differentials behave?". Let me explain this by way of an analogy. Suppose I teach you all the rules for adding and multiplying …

Jul 21, 2018 · 75 can someone please informally (but intuitively) explain what "differential form" mean? I know that there is (of course) some formalism behind it - definition and possible operations with …

I have a hazy notion of some stuff in differential geometry and a better, but still not quite rigorous understanding of basics of differential topology. I have decided to fix this lacuna once for ...

Nov 3, 2016 · What bothers me is this definition is completely circular. I mean we are defining differential by differential itself. Can we define differential more precisely and rigorously? P.S. Is it possible to …

Next semester (fall 2021) I am planning on taking a grad-student level differential topology course but I have never studied differential geometry which is a pre-requisite for the course. My plan i...

May 15, 2012 · Does there exist any correspondence between difference equations and differential equations? In particular, can one cast some classes of ODEs into difference equations or vice versa?

A linear partial differential operator is elliptic if it's principal symbol is a linear-space isomorphism for all nonzero covector fields $\omega\neq0\in\Gamma (T^*M)$. These notions also hold for nonlinear …

Solve the differential equation using Taylor-series expansion Ask Question Asked 13 years, 7 months ago Modified 13 years, 7 months ago

Nov 29, 2015 · The meaning of the notation is indeed a second order differential, i.e. a difference of difference, not a squared difference. Then about any function will show you that the square of the …