Interchange and g in Equation (10) to obtain a similar formula. Then subtract this formula from Equation (10) to show that This equation is

Interchange ƒ and g in Equation (10) to obtain a similar formula. Then subtract this formula from Equation (10) to show that

This equation is Green’s second formula.

Data from Exercise 29

Suppose that ƒ and g are scalar functions with continuous first- and second-order partial derivatives throughout a region D that is bounded by a closed piecewise smooth surface S. Show that

Equation (10) is Green’s first formula.

S (fVggVf) n do: = fff or D (fVg - gf) dV. (11)