What actually is a differential? - Mathematics Stack Exchange I am a bit confused about differentials, and this is probably partly due to what I find to be a rather confusing teaching approach (I know there are a bunch of similar questions around, but none o
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
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
How to derive a differential equation of an ellipse I am quite new to differential equations and derivatives I want to derive an differential form for equation of an ellipse If i start with an ordinary ellipse equation \\begin{equation} \\frac{x^2}
Why can we treat differential operators as if they behave like . . . Then one thinks of differential operators as a linear maps between such spaces Often the space of all linear maps between two spaces is itself a vector space and so one can indeed start to manipulate differential operators as if they are ‘objects’ in their own right eg add them together