---
tags : Mechanics,Mathmatics
title : 2020.4.7(7)
---
# Mechanics (7)
## Conclusion of words in subject 3
### Contour integral
We call a line integration of one cercuit in closed path C as **Contour Integration**.
ex)

$\huge \oint_C \mathbf{F} \cdot d\mathbf{r}$

($C$ means the initial of "contour")

### Nabla

We can write $\large \frac{\partial f_x}{\partial y} = \frac{\partial f_y}{\partial x} , \frac{\partial f_y}{\partial z} = \frac{\partial f_z}{\partial y} , \frac{\partial f_z}{\partial x} = \frac{\partial f_x}{\partial z}$ by bector differential opelater $\nabla$.

$\huge \nabla \equiv i\frac{\partial }{\partial x} + j\frac{\partial }{\partial y} + k\frac{\partial }{\partial z}$

$\huge F = -\nabla U(r)$