Compute the gradient of the following 2D scaler functions:a. ∅ = −2????(??2 + ??2)b. ∅ = −????+ ????c. ∅ = 2????2- Compute the divergence of the gradients of ∅ in question 13- Compute the curl of the gradients of ∅ in question 14- For ?? = (?? + ??)??⃗+ (?? + ??)??⃗+ (??2 + ??2 + ??2)??? ⃗ find the component of rotation at(2,2,2) 1- Compute the gradient of the following 2D scaler functions:a. Ø = -2ln(x? + y?)b. Ø = -Ux + vyc. Ø = 2yx2- Compute the divergence of the gradients of Ø in question 13- Compute the curl of the gradients of Ø in question 14- For q = (x + y)ỉ + (y + z)j+ (x² + y² + z²)k find the component of rotation at(2,2,2)

As per the guidelines I solved your first question complete ( with all three subparts). For more…

Answered: 1- Compute the gradient of the…

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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Compute the gradient of the following 2D scaler functions:
a. ∅ = −2????(??2 + ??2)
b. ∅ = −????+ ????
c. ∅ = 2????
2- Compute the divergence of the gradients of ∅ in question 1
3- Compute the curl of the gradients of ∅ in question 1
4- For ?? = (?? + ??)??⃗+ (?? + ??)??⃗+ (??2 + ??2 + ??2)??? ⃗ find the component of rotation at
(2,2,2)

1- Compute the gradient of the following 2D scaler functions:
a. Ø = -2ln(x? + y?)
b. Ø = -Ux + vy
c. Ø = 2yx
2- Compute the divergence of the gradients of Ø in question 1
3- Compute the curl of the gradients of Ø in question 1
4- For q = (x + y)ỉ + (y + z)j+ (x² + y² + z²)k find the component of rotation at
(2,2,2)

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