Jul 21, 2018 · 68 can someone please informally (but intuitively) explain what "differential form" mean? I know that there is (of course) some formalism behind it - definition and possible …

1 @Alexey ∫R g(x)dx ∫ R g (x) d x probably means integration of g g with respect to the Lebesgue measure (or a different implicitly given measure) here. The measure μ μ is then defined by its …

2 One could define a linear differential equation as one in which linear combinations of its solutions are also solutions.

Aug 19, 2015 · Differential forms are things that live on manifolds. So, to learn about differential forms, you should really also learn about manifolds. To this end, the best recommendation I …

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

The differential equations class I took as a youth was disappointing, because it seemed like little more than a bag of tricks that would work for a few equations, leaving the vast majority of …

This (the formula for the derivative of the metric tensor) seems to be a direct consequence of corrollary 7 in chapter 6 of the second volume of Spivak's comprehensive introduction to …

Jul 13, 2015 · The differential of a function at is simply the linear function which produces the best linear approximation of () in a neighbourhood of . Specifically, among the linear functions that …

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 …

Sep 7, 2023 · A differential k k -form is what I have been thinking a k k -form is, that is, an alternating covariant tensor field of degree k k. Some people omit "differential" for some …