Jul 13, 2015 · The differential of a function $f$ at $x_0$ is simply the linear function which produces the best linear approximation of $f(x)$ in a neighbourhood of $x_0$.

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 …

Mar 4, 2020 · At this point, however, I think that the best way to approach the daunting concept of differential forms is to realize that differential forms are defined to be the thing that makes …

Nov 29, 2015 · The meaning of the notation is indeed a second order differential, i.e. a difference of difference, not a squared difference. Then about any function will show you that the square …

For mathematics departments, some more strict books may be suitable. But whatever book you are using, make sure it has a lot of solved examples. And ideally, it should also include some …

Nov 19, 2014 · $\begingroup$ And here is one more example, which comes to mind: a book for famous Russian mathematician: Ordinary Differential Equations, which does not cover that …

Oct 29, 2011 · What is the difference between an implicit ordinary differential equation and a differential algebraic equation? 2 Explicit formula for the implicit Euler method

Next semester (fall 2021) I am planning on taking a grad-student level differential topology course but I have never studied differential geometry which is a pre-requisite for the course. My plan …

Apr 30, 2020 · with $\boldsymbol{\kappa}=i\mathbf{k}.$ This multiplication by $\mathcal L$ is the Fourier-space version of the differential operator from $(1)$. Notice that $\mathcal L$ is just a …

You made it clear that F(y/x) will imply that it is a division of 2 homogeneous equations of the same degree, but how does that imply that it is also the first differential dy/dx of a certain …