3. Green's first formula Suppose that f and g are scalar func- tions with continuous first- and second-order partial derivatives throughout a region D that is bounded by a closed piecewise smooth surface S. Show that /| f Vg•n do = /| (fV²g + Vf•Vg) dV. (10) Equation (10) is Green's first formula. (Hint: Apply the Diver- gence Theorem to the field F = f Vg.)
3. Green's first formula Suppose that f and g are scalar func- tions with continuous first- and second-order partial derivatives throughout a region D that is bounded by a closed piecewise smooth surface S. Show that /| f Vg•n do = /| (fV²g + Vf•Vg) dV. (10) Equation (10) is Green's first formula. (Hint: Apply the Diver- gence Theorem to the field F = f Vg.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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