A3. (i) Show that the derivative of the following distribution T = H (x) - 2H(2-x) where H(x) is the Heaviside step function, is do +262. (ii) Given the following function f(t) = t>0 t<0 fe-t |-et show that its distribution derivative is given by 28+ h, where h = −e-||

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A3.
(i) Show that the derivative of the following distribution
T = H (x) — 2H (2 - x)
where H(x) is the Heaviside step function, is do +282.
(ii) Given the following function
f(t) =
t> 0
t < 0
-et
show that its distribution derivative is given by 26 +h, where he¯|t|.
=
Transcribed Image Text:A3. (i) Show that the derivative of the following distribution T = H (x) — 2H (2 - x) where H(x) is the Heaviside step function, is do +282. (ii) Given the following function f(t) = t> 0 t < 0 -et show that its distribution derivative is given by 26 +h, where he¯|t|. =
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