In Cartesian coordinates, a vector field takes the form F = 2rz i+ 2yz j+ (z + y?) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r,ó, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a).

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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In Cartesian coordinates, a vector field takes the form
F = 2rz i+ 2yzj+(r² + y?) k
throughout the whole of three-dimensional space.
(a) Find the divergence and curl of F in Cartesian coordinates.
(b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates
(r, 0, z).
(c) Use your answer to part (b) to calculate the divergence and curl of F in
cylindrical coordinates. Comment on the agreement with part (a).
Transcribed Image Text:In Cartesian coordinates, a vector field takes the form F = 2rz i+ 2yzj+(r² + y?) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, 0, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a).
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