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 October 18th, 2019, 12:24 AM #1 Member   Joined: Dec 2018 From: Amsterdam Posts: 38 Thanks: 2 Gradient and it's effect in math and statistics? I have a very basic understanding of what a gradient is, but what is it's effect in math and statistics? (I know this question is maybe to broad) October 18th, 2019, 02:21 AM #2 Senior Member   Joined: Dec 2015 From: Earth Posts: 827 Thanks: 113 Math Focus: Elementary Math Vectorial Analysis . https://en.wikipedia.org/wiki/Vector...tial_operators For example $\displaystyle \nabla \vec{F}$ measures the rate and direction of change in a scalar field F. also you may find the gradient in some books written as grad(f). Thanks from jenniferruurs Last edited by idontknow; October 18th, 2019 at 02:25 AM. October 18th, 2019, 04:46 AM #3 Senior Member   Joined: Jun 2019 From: USA Posts: 380 Thanks: 205 Physically, a number of processes depend on the gradient of a field (how quickly it changes in space, and in what direction). For example, in heat conduction, the heat flux is proportional to the gradient of the temperature field $-\vec{\nabla}T$. In diffusion of solutions, the diffusion flux is proportional to the gradient of the concentration field $-\vec{\nabla}C$. Pressure gradients in fluids (or solids, for that matter) produce a force per unit volume $f=-\vec{\nabla}P$. The gradient is also used in some numerical approximation methods for finding minima and maxima of functions, among other things. Incidentally, you can also take the gradient of a vector field, although this gives you a second-order tensor. For example, the stress tensor in Newtonian fluids is proportional to $\vec{\nabla}\vec{u}$. Thanks from idontknow and jenniferruurs Tags effect, gradient, math, statistics Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post 3uler Math 7 February 27th, 2015 08:26 AM kingkos Probability and Statistics 1 March 26th, 2013 09:48 AM kingkos Probability and Statistics 1 December 6th, 2012 01:41 PM qfreddy95 Probability and Statistics 12 May 6th, 2011 04:57 PM danield3 Probability and Statistics 2 May 13th, 2010 12:48 PM

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