User:Majkelx/sandbox

Non-trivial calculation rules

 * 1)  $$\operatorname{div}  \, \operatorname{grad} f          \equiv \nabla \cdot  \nabla f \equiv \nabla^2 f$$
 * 2)  $$\operatorname{curl} \, \operatorname{grad} f          \equiv \nabla \times \nabla f = \mathbf 0$$
 * 3)  $$\operatorname{div}  \, \operatorname{curl} \mathbf{A} \equiv \nabla \cdot  (\nabla \times \mathbf{A}) = 0$$
 * 4)  $$\operatorname{curl} \, \operatorname{curl} \mathbf{A} \equiv \nabla \times (\nabla \times \mathbf{A}) = \nabla (\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A}$$ (Lagrange's formula for del)
 * 5)  $$\nabla^2 (f g) = f \nabla^2 g + 2 \nabla f \cdot \nabla g + g \nabla^2 f$$