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OF 2. Use the above to find 3, i.e the rate of change of F relative to du. Evaluate your answer at (u, v) = (1,0) to see if the numbers make sense to you.

OF 2. Use the above to find 3, i.e the rate of change of F relative to du. Evaluate your answer at (u, v) = (1,0) to see if the numbers make sense to you.

Advanced Engineering Mathematics
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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Suppose that the function F(x, y, z) has the gradient vector field grad (F) = ( OF OF OF dx' dy' dz Let T(u, v) be the transformation = (y+z,x+z, x + y). x(u, v) = u cos(v), y(u, v) = u sin(v), z(u, v) = v. Just #2 1. Compute the vector fields Ou, dy and the Jacobi matrix of T. 2. Use the above to find , i.e the rate of change of F relative to du. Evaluate your answer at (u, v) = (1,0) to see if the numbers make sense to you. 3. Use the above to find , i.e the rate of change of F relative to du. Evaluate your answer at θυ (u, v) = (1, 0) to see if the numbers make sense to you.
Transcribed Image Text:Suppose that the function F(x, y, z) has the gradient vector field grad (F) = ( OF OF OF dx' dy' dz Let T(u, v) be the transformation = (y+z,x+z, x + y). x(u, v) = u cos(v), y(u, v) = u sin(v), z(u, v) = v. Just #2 1. Compute the vector fields Ou, dy and the Jacobi matrix of T. 2. Use the above to find , i.e the rate of change of F relative to du. Evaluate your answer at (u, v) = (1,0) to see if the numbers make sense to you. 3. Use the above to find , i.e the rate of change of F relative to du. Evaluate your answer at θυ (u, v) = (1, 0) to see if the numbers make sense to you.
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