It can be shown that for arbitrary b, 8(bx): 8(x) You can assume these results for this part of the question: i) Consider a function g(x) with one simple root at x = xo. Show that 8(g(x)) = = (a), and more generally, 8(b(x − x)) 8(x-xo) = |b| 8(x-xo) g'(xo)| ii) Now briefly describe how this result can be generalised to g(x) with n simple roots at {x₁,x₂,...,xn}.
It can be shown that for arbitrary b, 8(bx): 8(x) You can assume these results for this part of the question: i) Consider a function g(x) with one simple root at x = xo. Show that 8(g(x)) = = (a), and more generally, 8(b(x − x)) 8(x-xo) = |b| 8(x-xo) g'(xo)| ii) Now briefly describe how this result can be generalised to g(x) with n simple roots at {x₁,x₂,...,xn}.
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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Question
Please answer the 2nd image, part ii) - using the last part of part i)
Transcribed Image Text:The Dirac delta-function obeys
for any function f(x).
** f(x)8(x − xo)dx = f(xo)
-∞
Transcribed Image Text:It can be shown that for arbitrary b, 8(bx):
You can assume these results for this part of the question:
i) Consider a function g(x) with one simple root at x = xo. Show that 8(g(x)) =
8(x)
(a), and more generally, 8(b(x − x))
=
8(x-xo)
= |b|
8(x-xo)
g'(xo)|
ii) Now briefly describe how this result can be generalised to g(x) with n simple roots at
{x₁,x₂,...,xn}.
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