ベクトル解析の公式の一覧
回転
∇ × A = ( 1 r ∂ A z ∂ θ − ∂ A θ ∂ z ) e r + ( ∂ A r ∂ z − ∂ A z ∂ r ) e θ + [ 1 r ∂ ∂ r ( r A θ ) − 1 r ∂ A r ∂ θ ] e z {\displaystyle \mathbf {\nabla } \times \mathbf {A} =\left({\frac {1}{r}}{\frac {\partial A_{z}}{\partial \theta }}-{\frac {\partial A_{\theta }}{\partial z}}\right)\mathbf {e} _{r}+\left({\frac {\partial A_{r}}{\partial z}}-{\frac {\partial A_{z}}{\partial r}}\right)\mathbf {e} _{\theta }+\left[{\frac {1}{r}}{\frac {\partial }{\partial r}}(rA_{\theta })-{\frac {1}{r}}{\frac {\partial A_{r}}{\partial \theta }}\right]\mathbf {e} _{z}}
ラプラシアン (スカラー場)