# Christoffel Symbols

## Homework Statement

Find the Christoffel symbols of a surface in the form $g=f(u,v).$

## Homework Equations

$f_{u_1u_1} = \Gamma^1_{11} f_{u_1} + \Gamma^2_{11}f_{u_2} + A \vec{N}$
$f_{u_1u_2} = f_{u_2u_1} = \Gamma^1_{12} f_{u_1} + \Gamma^2_{12}f_{u_2} + B \vec{N}$
$f_{u_2u_2} = \Gamma^1_{22} f_{u_1} + \Gamma^2_{22}f_{u_2} + C\vec{N}$

## The Attempt at a Solution

I know how to calculate the Christoffel symbols if it explicitly shows a parameterized surface but how can I calculate it of the form $g=f(u,v)$?

I just need help getting started. Thanks for your time!