What is a differential form? - Mathematics Stack Exchange 69 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 differential forms, but what is the motivation of introducing and using this object (differential form)?
real analysis - Rigorous definition of differential - Mathematics . . . 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 define differential simply as the limit of a difference as the difference approaches zero?: $$\mathrm {d}x= \lim_ {\Delta x \to 0}\Delta x$$ Thank you in advance
calculus - The second differential versus the differential of a . . . Is the above definition of the second differential used today in mathematics? This is the question for which I will accept an answer Can the above definition be brought into consonance with the definition of the differential of a differential form? Which, as I understand it goes as follows:
integration - Explanation for the integral of differential forms . . . Once I heard differential forms being introduced in a classroom as "the stuff we want to integrate" Take a look at the change of variables formula for integration in $\mathbb {R}^n$ (the Jacobian formula) and you will see it behaves the way differential forms do