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 …

Jul 8, 2018 · Now if you want to, you can partially evaluate the second differential $ \mathrm d ^ 2 y $ when $ \mathrm d ^ 2 x = 0 $, getting a partial second differential showing only the …

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 …

Oct 6, 2020 · $\begingroup$ Everything I see online is about exact differential equations where you have something dx + something dy and if you take the derivative of the first piece with …

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

Integral and differential calculus, after a good (and mathematically correct) explanation of the two. 1.

In my AI textbook there is this paragraph, without any explanation. The sigmoid function is defined as follows $$\sigma (x) = \frac{1}{1+e^{-x}}.$$ This function is easy to differentiate

Jan 24, 2023 · $\begingroup$ Much of differential geometry has merged into geometric analysis (as opposed to local geometric computations). There are lots of different analytic tools you …