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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). 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 secondorder tensor. For example, the stress tensor in Newtonian fluids is proportional to $\vec{\nabla}\vec{u}$. 

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