Vector Calculus

The gradient \(\nabla\) (vector). \[grad(f) = \nabla f = \frac{\partial f}{\partial x} . \vec{i} + \frac{\partial f}{\partial y} . \vec{j} +\frac{\partial f}{\partial z} . \vec{k}\]

Divergence \(\nabla \cdot\) (scalar) \[div(f) = \nabla \cdot f = \frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} +\frac{\partial f}{\partial z}\]

Laplacian \(\Delta\) : \[\Delta f = (\nabla \cdot \nabla) f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} +\frac{\partial^2 f}{\partial z^2}\]