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What exactly is a differential? - Mathematics Stack Exchange 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 rational numbers Then you ask me "But what are the rational numbers?" The answer is: They are anything that obeys those rules Now in order for that to make sense, we have to know that there's at least
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:
reference request - Best Book For Differential Equations? - Mathematics . . . The differential equations class I took as a youth was disappointing, because it seemed like little more than a bag of tricks that would work for a few equations, leaving the vast majority of interesting problems insoluble Simmons' book fixed that