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 …

Also, notice an interesting reversal: originally, differentials came first, and they were used to define the derivative as a ratio. Today, derivatives come first (defined as limits), and …

Nov 3, 2016 · Without knowing want a linear transformation is, (which, I would say, is the minimum requirement for giving a rigorous definition of differentials, if one dose not want to run …

Nov 29, 2015 · Just wondering, is this valid: $$ \\left(\\frac{df}{dx}\\right)^2=\\frac{d^{2}f}{dx^{2}} $$

Oct 3, 2019 · 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 …

Jul 22, 2015 · I see the differential operator both with upright and italic d in different books/articles. So I'm curious about $$ \\int x^2 \\, dx \\quad \\text{vs.} \\quad \\int x ...

May 25, 2015 · Math isn't linear. There are lots of directions you can go in once you're past the usual calculus sequence (and, at least in theory, you could start these courses before finishing …

May 14, 2016 · Basically, this is saying "manipulating differentials is perfectly okay, but you are supposing that these things are differentiable instead of proving it". If you are doing a proof …

Interpreting higher order differentials Ask Question Asked 11 years, 4 months ago Modified 11 years, 4 months ago

The seemingly endless number of vague conceptions of "differentials" bothered me a great deal when I first learned calculus -- so much so that I spent an inordinate amount of time thinking …