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QI) Determine the gradient of the following scalar field V = e(2x+3y)cos5z

QI) Determine the gradient of the following scalar field V = e(2x+3y)cos5z

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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ull Zain JO ☺ 4:47 AM O 66% EE202_HW2_2020_2 Homework Q1) Determine the gradient of the following scalar field V = e(2x+3y) cos5z Q2) Given f = x²y + 3z + 4, find (i) Vf. (ii) V² f, and (iii) a unit normal to f= 0 at (1, -2, 4). Q3) Find the divergence and curl of the following vectors: А 3D еху а, +sinxy a, + cos? xz a, Q4) Given the vector field R %3 (2x?у + yz)a, + (ху? — хz")а, + (схуг — 2х?у?)а, Determine the value of e for R to be solenoidal. (Note: solenoidal means the divergence equal to zero) 05) If the vector field т 3 (аху + Bz3)а, + (3x? — үг)а, + (3xz? — у)а, is irrotational, determine a, B, and y. Find V-T at (2, -1, 0). (Note: irrotational means the curl equal to zero)
Transcribed Image Text:ull Zain JO ☺ 4:47 AM O 66% EE202_HW2_2020_2 Homework Q1) Determine the gradient of the following scalar field V = e(2x+3y) cos5z Q2) Given f = x²y + 3z + 4, find (i) Vf. (ii) V² f, and (iii) a unit normal to f= 0 at (1, -2, 4). Q3) Find the divergence and curl of the following vectors: А 3D еху а, +sinxy a, + cos? xz a, Q4) Given the vector field R %3 (2x?у + yz)a, + (ху? — хz")а, + (схуг — 2х?у?)а, Determine the value of e for R to be solenoidal. (Note: solenoidal means the divergence equal to zero) 05) If the vector field т 3 (аху + Bz3)а, + (3x? — үг)а, + (3xz? — у)а, is irrotational, determine a, B, and y. Find V-T at (2, -1, 0). (Note: irrotational means the curl equal to zero)
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