le can define an operator * : 2'(R?) n'(R?) by defining *dx = dy and *dy = -dx, and extending nearly. If f: RR is a 0-form, show that d* (df) = 2 ) ds Ady.
le can define an operator * : 2'(R?) n'(R?) by defining *dx = dy and *dy = -dx, and extending nearly. If f: RR is a 0-form, show that d* (df) = 2 ) ds Ady.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 28E
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![We can define an operator * : 2'(R?) → N'(R?) by defining +dx = dy and *dy = -dx, and extending
linearly. If f : RR is a 0-form, show that
af af
d (d f):
) dx Ady.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9610a00a-c07a-4857-a98c-5ee0247b3ec6%2F5c6b2f1b-fb07-4ed8-a114-581414500ac6%2Fuv4v7vir_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We can define an operator * : 2'(R?) → N'(R?) by defining +dx = dy and *dy = -dx, and extending
linearly. If f : RR is a 0-form, show that
af af
d (d f):
) dx Ady.
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