The Laplacian of a function f of n variables ¤1, x2, · ·· ¤n, denoted V² ƒ is defined by V² f (#1, ®2, · · • , xn):= a² f _ в ƒ Now assume that f depends only on r wherer = (x² + æ; + · .. + x%)³, i.e. ƒ (x1, æ2,·.,æn) = 9 (r), for some function g. Show that, for ¤1, ¤2, · ·' , ¤n #0, v°f = ",'d (-) + s" ()
The Laplacian of a function f of n variables ¤1, x2, · ·· ¤n, denoted V² ƒ is defined by V² f (#1, ®2, · · • , xn):= a² f _ в ƒ Now assume that f depends only on r wherer = (x² + æ; + · .. + x%)³, i.e. ƒ (x1, æ2,·.,æn) = 9 (r), for some function g. Show that, for ¤1, ¤2, · ·' , ¤n #0, v°f = ",'d (-) + s" ()
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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