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 …

A differential equation is linear if and only if it is in the following form or is mathematically equivalent to said form: a(x)*y + b(x)*y' + c(x)*y'' + ... = q(x) (Right side is just a loose function …

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 …

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 …

Mar 18, 2013 · There is a formula of computing exterior derivative of any differential form (which is assumed to be smooth). In your case, if $\sigma$ is a 1-form, and $$ \sigma = \sum_{j=1}^n …

Dec 23, 2018 · $\begingroup$ Well, I saw this equation in a fb group named JulioProfe some time ago. I found the exercise interesting and decided to take it back a few days ago, I don't know …

Aug 25, 2015 · If you have a differential equation with no partial derivatives (i.e., all the equation's derivatives are total), you have an ODE. (Annoyingly for this terminology, one can also refer to …

Nov 3, 2016 · Of course, defining $$ \mathrm{d}x= \lim_{\Delta x \to 0}\Delta x $$ is the same as defining $$ dx=0, $$ which makes no sense.

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