We can also define a derivative in terms of differentials as the ratio of differentials of function by the differential of a variable. May 10, 2018 · I was attempting to solve the following integro-differential equation using convolutions. ), as well as for some integral equations, a rule of thumb is the following: the equation is called autonomous when for any of its solutions any (admissible) time translate of that solution is its solution, too. Nov 3, 2016 · I mean we are defining differential by differential itself. Specifically, among the linear functions that take the value at , there exists at most one such that, in a neighbourhood of , we have: It is the linear map that we call the differential of at and denote . My answer also had a convolution which did not seem right and was wondering if someone would check my proce. Use (symplectic-geometry), (riemannian For questions about ordinary differential equations, which are differential equations involving ordinary derivatives of one or more dependent variables with respect to a single independent variable. Can we define differential more precisely and rigorously? P. Mar 5, 2019 · For differential equations (ordinary, partial, with deviating argument, etc. In simple words, the rate of change of function is called as a derivative and differential is the actual change of function. Modern differential geometry focuses on "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such structures, use (differential-topology) instead. Dec 30, 2025 · How to solve this Ordinary Differential Equation? Ask Question Asked 19 days ago Modified 17 days ago Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). See this answer in Quora: What is the difference between derivative and differential?. Jul 13, 2015 · 8 The differential of a function at is simply the linear function which produces the best linear approximation of in a neighbourhood of . Is it possible to define differential simply as the limit of a difference as the difference approaches zero?: dx = limΔx→0 Δx d x = lim Δ x → 0 Δ x Thank you in advance. S. My answer also had a convolution which did not seem right and was wondering if someone would check my proce Jul 13, 2015 · 8 The differential of a function at is simply the linear function which produces the best linear approximation of in a neighbourhood of . EDIT: I still think I didn't catch the best Jul 21, 2018 · 72 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 operations with differential forms, but what is the motivation of introducing and using this object (differential form)? Oct 3, 2019 · To define a differential a little more rigorously, let's say that every equation/relation has a foundational independent variable that all the others are ultimately dependent upon, even if we don't name it. For questions specifically concerning partial differential equations, use the [tag:pde] instead.

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