The following are important identities involving derivatives and integrals in vector calculus. See more

Gradient
For a function $${\displaystyle f(x,y,z)}$$ in three-dimensional Cartesian coordinate variables, the gradient is the vector field:
where i, j, k are the standard unit vectors for the x, y, z-axes. … See more

Divergence of curl is zero
The divergence of the curl of any continuously twice-differentiable vector field A is always zero:
This is a special case … See more

• Comparison of vector algebra and geometric algebra
• Del in cylindrical and spherical coordinates – Mathematical gradient operator in certain coordinate systems
• Differentiation rules – Rules for computing … See more

For scalar fields $${\displaystyle \psi }$$, $${\displaystyle \phi }$$ and vector fields $${\displaystyle \mathbf {A} }$$,
Distributive properties See more

Differentiation
Gradient
• $${\displaystyle \nabla (\psi +\phi )=\nabla \psi +\nabla \phi }$$
• See more

• Balanis, Constantine A. (23 May 1989). Advanced Engineering Electromagnetics. ISBN 0-471-62194-3.
• Schey, … See more