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![[tex] \nabla ^u \nabla_u \phi = g^{ij} \Big( \frac{\partial ^2 \phi}{\partial x^i \partial x^j} - \Gamma^{k}_{ij} \frac{\partial \phi}{\partial x^k} \Big)\\\\\frac{\partial \sigma^{ij}}{\partial x^i} + \sigma^{kj} \Gamma^i _{ki} + \sigma^{ik} \Gamma^j _{ki} = 0[/tex]](images/latex/99f2e51931163431f7feb4825fc711ebccd99981_0.png "[tex] \nabla ^u \nabla_u \phi = g^{ij} \Big( \frac{\partial ^2 \phi}{\partial x^i \partial x^j} - \Gamma^{k}_{ij} \frac{\partial \phi}{\partial x^k} \Big)\\\\\frac{\partial \sigma^{ij}}{\partial x^i} + \sigma^{kj} \Gamma^i _{ki} + \sigma^{ik} \Gamma^j _{ki} = 0[/tex]")
![[tex]\nabla^2 f = \sum_{i=1}^{n} \nabla^2 f_i e_i[/tex]](images/latex/7ecc5c399511fd2bcc1714daf97f396c1ead5e3d_0.png "[tex]\nabla^2 f = \sum_{i=1}^{n} \nabla^2 f_i e_i[/tex]")
![[tex] \overrightarrow { \nabla ^2 \vec {f (\vec {x}) } } = \sum_{n=1}^3 \nabla^2 f_n \hat{x}_n = (\nabla ^2 f_1, \nabla ^2 f_2, \nabla ^2 f_3)[/tex]](images/latex/e408349536121afb29883cb1faa234d21c7f4ace_0.png "[tex] \overrightarrow { \nabla ^2 \vec {f (\vec {x}) } } = \sum_{n=1}^3 \nabla^2 f_n \hat{x}_n = (\nabla ^2 f_1, \nabla ^2 f_2, \nabla ^2 f_3)[/tex]")
![[tex] \nabla ^2 f_n = \sum_{i=1}^3 \frac {\partial^2 f_n}{\partial x_i^2} [/tex]](images/latex/db2f84bbe5797c798e25c65557d9e44f0ebb1524_0.png "[tex] \nabla ^2 f_n = \sum_{i=1}^3 \frac {\partial^2 f_n}{\partial x_i^2} [/tex]")
![[tex] \overrightarrow { \nabla ^2 \vec {f (\vec {x}) } } = \nabla ( \nabla \vec { f (\vec {x})} ) - \nabla \times (\nabla \times \vec {f (\vec {x})}) [/tex]](images/latex/b4f77d909f524973722efe5e60166b403b15a2da_0.png "[tex] \overrightarrow { \nabla ^2 \vec {f (\vec {x}) } } = \nabla ( \nabla \vec { f (\vec {x})} ) - \nabla \times (\nabla \times \vec {f (\vec {x})}) [/tex]")
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