Question

write mathematical forms of gradient of a scalar function, divergence and curl of a vector​

Answer 1

Answer:

Gradient :

For a real-valued function f(x,y,z) on R3 , the gradient ∇f(x,y,z) is a vector-valued function on R3 , that is, its value at a point (x,y,z) is the vector

∇f(x,y,z)=(∂f∂x,∂f∂y,∂f∂z)=∂f∂xi+∂f∂yj+∂f∂zk

in R3 , where each of the partial derivatives is evaluated at the point (x,y,z) .

it is often convenient to write the divergence div f as ∇⋅f ,

We can also write curl f in terms of ∇ , namely as ∇×f , since for a vector field f(x,y,z)=P(x,y,z)i+Q(x,y,z)j+R(x,y,z)k , we have:

curl f