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a. By directly evaluating the integral t ( f * 9) (t) = √² (e^t-e^(-3t))/5 the definition of f * g. e^(w)e^(-3(t-w)) dw = -1 b. By computing ¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}.

a. By directly evaluating the integral t ( f * 9) (t) = √² (e^t-e^(-3t))/5 the definition of f * g. e^(w)e^(-3(t-w)) dw = -1 b. By computing ¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}.

Advanced Engineering Mathematics
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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For the functions f(t)=et and g(t)=e−3t, defined on 0≤t<∞, compute f∗g in two different ways: 

a. By directly evaluating the integral in the definition of f * g. (f* g)(t) = (e^t-e^(-3t))/5 t S = e^(w)e^(-3(t-w)) dw b. By computing L-¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}. (f* g)(t) = L−¹ {F(s)G(s)} = L¯¹{ 1/5 1/s(e^t-e^-3t) = help (formulas)
Transcribed Image Text:a. By directly evaluating the integral in the definition of f * g. (f* g)(t) = (e^t-e^(-3t))/5 t S = e^(w)e^(-3(t-w)) dw b. By computing L-¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}. (f* g)(t) = L−¹ {F(s)G(s)} = L¯¹{ 1/5 1/s(e^t-e^-3t) = help (formulas)
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