11 июн. 2012 г. · The gradient of a vector field corresponds to finding a matrix (or a dyadic product) which controls how the vector field changes as we move from ...

28 окт. 2012 г. · The gradient operator takes a function between two vector spaces U and V, and returns another function which, when evaluated at a point in U, gives a linear ...

11 мар. 2015 г. · By definition, if ϕ is a scalar function of ϕ(x,y,z), then ∇ϕ=∂ϕ∂xi+∂ϕ∂yj+∂ϕ∂zk.

26 апр. 2016 г. · In Multivariable Calculus, we can easily find the gradient of a scalar function (producing a scalar field) f:Rn→R, and the gradient function ...

5 окт. 2016 г. · Let f,g be differentiable vector functions, and let B(⋅,⋅) be a bilinear function. Then D[B(f,g)](x)v=B(D[f](x)v,g(x))+B(f(x),D[g](x)v).

7 мар. 2019 г. · Let a=(a,b,c), so that aTx=ax+by+cz. Then. ∇x(aTx)=(∂∂x(ax+by+cz),∂∂y(ax+by+cz),∂∂z(ax+by+cz))=(a,b,c). Geometric interpretation:.

16 янв. 2018 г. · In order to take "gradients" of vector fields, you'd need to introduce higher order tensors and covariant derivatives, but that's another story.

24 мая 2014 г. · First, ∇⋅→r=3. This is a general and useful identity: that the divergence of the position vector is just the number of dimensions.

12 дек. 2018 г. · First of all, since the dipole m on which the force acts is constant, the formula simplifies to F=∇(m⋅B)=mTJB=JTBm,.

22 сент. 2017 г. · The gradient of a gradient is commonly called the second derivative. A hill with a constant slope has a gradient, but the gradient of the gradient is zero.