Manipulating Equations with Del Operators

[dm164]

I'm trying to understand how to manipulate equations with del operators.

If I have a equation like :

div( A + B ) = div(E)
and assume A,B,E are twice differential vectors

do div cancel?

can I say E = A + B?

If I write is like this
div( A + B - E ) = 0
div( A + B - (A + B)) = 0
div( 0 ) = 0.

but div( constant ) = 0 also

 

[Stephen Tashi]

Look at examples of vector fields that are constant. A+B might be one constant field with a zero divergence and E might be a different one.

 

[lavinia]

I'm trying to understand how to manipulate equations with del operators.

If I have a equation like :

div( A + B ) = div(E)
and assume A,B,E are twice differential vectors

do div cancel?

can I say E = A + B?

if the divergence of a vector field is zero then it is the curl of another vector field.