Let ø = p(x), u = u(x), and T = T(x) be differentiable scalar, vector, and tensor fields, where x is the position vector. Show that %3D div (Tu) = u · div T + tr (T grad u)
Let ø = p(x), u = u(x), and T = T(x) be differentiable scalar, vector, and tensor fields, where x is the position vector. Show that %3D div (Tu) = u · div T + tr (T grad u)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let ø = p(x), u = u(x), and T = T(x) be differentiable scalar, vector, and tensor fields, where x is the position
vector. Show that
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedadeb2e-cdac-43d1-98ad-015a8ab931d0%2Feaf6336a-e723-42bf-8272-f226baff7fb6%2Fr6110gh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let ø = p(x), u = u(x), and T = T(x) be differentiable scalar, vector, and tensor fields, where x is the position
vector. Show that
%3D
![div (Tu) = u · div T + tr (T grad u)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedadeb2e-cdac-43d1-98ad-015a8ab931d0%2Feaf6336a-e723-42bf-8272-f226baff7fb6%2Fsaiy0im_processed.png&w=3840&q=75)
Transcribed Image Text:div (Tu) = u · div T + tr (T grad u)
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