Page 446 - Introduction to Continuum Mechanics

430 Integral Formulation of General Principles

Fig. 7,2

7.2 Divergence Theorem

Let v = v 1(x xy)e 1+V2(jt,y)e2 be a vector field. Applying Eqs. (7.1.1) and (7.1.2) to vj and v 2
and adding, we have

In indicial notation, Eq. (7.2. la) becomes

and in invariant notation,

The following generalization not only appears natural, but can indeed be proven (we omit
the proof)

Or, in invariant notation,