What is the Laplacian of the following functions? (a) ƒ(z) = Acikz (b) ƒ (x, y, z) = A (x² + y² + z²) %3| 36 45 (c) f (x, y) = V(#+1)² +y² (d) ƒ (x,t) = Ae'(k# -wt).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4. What is the Laplacian of the following functions?
(a) f (2) = Acikz
(b) f (x, y, z) = A (x² + y² + z²)
(c) f (x, y) =
36
45
-
V (z+1)° +y² V
(d) ƒ (x,t) = Ae¿(kæ-wt)
/x² +(y-2)² ¨
Transcribed Image Text:4. What is the Laplacian of the following functions? (a) f (2) = Acikz (b) f (x, y, z) = A (x² + y² + z²) (c) f (x, y) = 36 45 - V (z+1)° +y² V (d) ƒ (x,t) = Ae¿(kæ-wt) /x² +(y-2)² ¨
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