# Differential of a 2-form

1. Apr 15, 2012

### tazzzdo

1. The problem statement, all variables and given/known data

Compute the differentials of the following form:

2. Relevant equations

f = exy dy ^ dz

3. The attempt at a solution

I'm a little confused on how to work with the wedge product. If I'm looking for df, should I start by calculating the dual f*? Or does the dual not come into play?

2. Apr 15, 2012

### HallsofIvy

Staff Emeritus
No, there is no reason to worry about the dual. For any f, $df= (\partial f/\partial x)dx+ (\partial f/\partial y)dy+ (\partial f/\partial z)dz$.

If
$f= e^{xy} dy^dz$ then
$$df= (\partial e^{xy}/\partial x)dx\^dy\^dz+ (\partial e^{xy}/\partial y)dy\^dy\^dz+ (\partial e^{xy}/\partial z)dz\^dy\^dz$$
Remember, of course, that the wedge product is "anti-symmetric".

3. Apr 15, 2012

### tazzzdo

So

df = yexy dx ^ dy ^ dz + xexy dy ^ dy ^ dz ? Is that the answer?

Last edited: Apr 15, 2012