Please work out the results of the following differential operations • Gradient of f (x, y, z) = x² + 4xy + 4y² – z2 - x + y? • Divergence of v (x, y, z) : = | x² – y² - хуz z2 • Laplacian of f (x, y, z) = x² + 4xy+ 4y x2 + y - • Curl of ú (x, y, z) = | x² – y² xyz

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 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Problem 1
Please work out the results of the following differential
operations
z?
• Gradient of f (x, y, z) = x² + 4xy + 4y²
x² + y
• Divergence of v (x, y, z) =
x² – y?
xyz
• Laplacian of f (x, y, z) = x² + 4xy+ 4y
x + y
• Curl of ú (x, y, z) =
| x² – y²
xyz
Transcribed Image Text:Problem 1 Please work out the results of the following differential operations z? • Gradient of f (x, y, z) = x² + 4xy + 4y² x² + y • Divergence of v (x, y, z) = x² – y? xyz • Laplacian of f (x, y, z) = x² + 4xy+ 4y x + y • Curl of ú (x, y, z) = | x² – y² xyz
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