In recent times, differential has become increasingly relevant in various contexts. 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. In this context, 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?
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)? calculus - What is the practical difference between a differential and ....
See this answer in Quora: What is the difference between derivative and differential?. In simple words, the rate of change of function is called as a derivative and differential is the actual change of function. We can also define a derivative in terms of differentials as the ratio of differentials of function by the differential of a variable. real analysis - Rigorous definition of "differential" - Mathematics ....
Furthermore, 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? 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 .... From another angle, 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: ordinary differential equations - difference between implicit and .... From another angle, what is difference between implicit and explicit solution of an initial value problem? Please explain with example both solutions (implicit and explicit)of same initial value problem? How to derive a differential equation of an ellipse.
From another angle, i am quite new to differential equations and derivatives. I want to derive an differential form for equation of an ellipse.
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