Compute the following Laplace transforms by hand using the definition of a Laplace trans- form (not using a table, although you can check your answers with a table): (a) Delta function: f(t) = 8(t) Note: the Laplace transform integral is from just before 0 (what you called 0 in calculus) to infinity. So, integrate from 0 to ∞. (b) Heaviside function: f(x) = {1; t≤0 1, 20 (c) Time-shifted delta function: f(t) = 8(t-a).

Compute the following Laplace transforms by hand using the definition of a Laplace trans- form (not using a table, although you can check your answers with a table): (a) Delta function: f(t) = 8(t) Note: the Laplace transform integral is from just before 0 (what you called 0 in calculus) to infinity. So, integrate from 0 to ∞. (b) Heaviside function: f(x) = {1; t≤0 1, 20 (c) Time-shifted delta function: f(t) = 8(t-a).

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

Compute the following Laplace transforms by hand using the definition of a Laplace trans-
form (not using a table, although you can check your answers with a table):
(a) Delta function: f(t) = 8(t)
Note: the Laplace transform integral is from just before 0 (what you called 0 in
calculus) to infinity. So, integrate from 0 to ∞.
0,
(b) Heaviside function: ƒ(z) = { 1 1,
(c) Time-shifted delta function: f(t) = 8(t-a).
t < 0
t≥0

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