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.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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