# DELETE THREAD need the latex code

1. Apr 27, 2005

### Phymath

$$\left\begin{array}{ccccccc}&q_1&q_2&q_3&h_1&h_2&h_3\\ carte&x&y&z&1&1&1 \\cylin&\rho&\phi&z&1&\rho&1 \\spher&r&\theta&\phi&1&r&rsin\ \theta \end{array}$$

$$\nabla f = \hat{e_1} \frac{1}{h_1}\frac{\partial f}{\partial q_1} + \hat{e_2} \frac{1}{h_2}\frac{\partial f}{\partial q_2} + \hat{e_3} \frac{1}{h_3}\frac{\partial f}{\partial q_3}$$

$$\hat{e_i} = \frac{1}{h_i}\frac{\partial \vect{r}}{\partial q_i} \ i = 1,2,3$$

$$\nabla \cdot \vect{A} = \frac{1}{h_1h_2h_3}\left(\partial_{q_1} (h_2h_3A_1) + \partial_{q_2}(h_1h_3A_2)+\partial_{q_3}(h_1h_2A_3))\right$$

$$\nabla \times \vect{A} = \frac{1}{h_1h_2h_3}\left(\begin{array}{ccc}\hat{e_1}h_1&\hat{e_2}h_2&\hat{e_3}h_3\\ \partial_{q_1}&\partial_{q_2}&\partial_{q_3}\\ h_1A_1&h_2A_2&h_3A_3\end{array}\right)$$

$$\nabla^2f = \frac{1}{h_1h_2h_3}\left(\frac{\partial}{\partial q_1}(\frac{h_2h_3}{h_1}\frac{\partial f}{\partial q_1})+\frac{\partial}{\partial q_2}(\frac{h_1h_3}{h_2}\frac{\parital f}{\partial q_2 })+\frac{\partial}{\partial q_3}(\frac{h_1h_2}{h_3}\frac{\partial f}{\partial q_3})\right)$$

Last edited: Apr 27, 2005