Metody matematyczne fizyki/Rachunek tensorowy: Różnice pomiędzy wersjami

<MATH>=\left[\left( {{\partial a_k}\over{\partial x^l}}-a_m{\Gamma^m}_{lk}\right)_{,n}-\left( {{\partial a_r}\over{\partial x^l}}-a_m{\Gamma^m}_{lr} \right){\Gamma^r}_{nk}-\left({{\partial a_k}\over{\partial x^s}}+a_m{\Gamma^m}_{sk}\right){\Gamma^s}_{ln}\right]+\;</MATH><BR>

<MATH>-\left[\left( {{\partial a_k}\over{\partial x^n}}-a_m{\Gamma^m}_{nk}\right)_{,l}- \left({{\partial a_r}\over{\partial x^n}}-a_m{\Gamma^m}_{nr}\right){\Gamma^r}_{lk}-\left({{\partial a_k}\over{\partial x^s}}-a_m{\Gamma^m}_{sk}\right){\Gamma^s}_{ln}\right]=\;</MATH><BR>

<MATH>=\left(a_{k,l,n}-a_{k,n,l}\right)+a_m\left({{\partial {\Gamma^m}_{nk}}\over{\partial x^l}}-{{\partial {\Gamma^m}_{lk}}\over{\partial x^n}}\right)+a_m\left({\Gamma^m}_{lr}{\Gamma^r}_{nk}-{\Gamma^m}_{nr}{\Gamma^r}_{lk}\right)\;</MATH>|2.90}}