6. Curl & Divergence: a) Calculate the 2D curl in F: F = < 4x³y, xy²+x+> b) Find the 2D divergence for F in part a. c) Is F in part a source free? Irrotational? Explain why. d) Compute the divergence for F = < 15x, -6y, -6z>. State what this means. e) Find the divergence of the vector field F= < x²yz, -xy²z, -xyz²> f) Compute the curl for F= < 3xz³ey2, 2xz³ ey², 3xz² ey² >
6. Curl & Divergence: a) Calculate the 2D curl in F: F = < 4x³y, xy²+x+> b) Find the 2D divergence for F in part a. c) Is F in part a source free? Irrotational? Explain why. d) Compute the divergence for F = < 15x, -6y, -6z>. State what this means. e) Find the divergence of the vector field F= < x²yz, -xy²z, -xyz²> f) Compute the curl for F= < 3xz³ey2, 2xz³ ey², 3xz² ey² >
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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
Transcribed Image Text:6. Curl & Divergence:
a) Calculate the 2D curl in F: F = < 4x³y, xy²+x+>
b) Find the 2D divergence for F in part a.
c) Is F in part a source free? Irrotational? Explain why.
d) Compute the divergence for F = < 15x, -6y, -6z>. State what this
means.
e) Find the divergence of the vector field F= < x²yz, -xy²z, -xyz²>
f) Compute the curl for F= < 3xz³ey2, 2xz³ ey², 3xz² ey² >
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