Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.9 The Convolution Integral - True-False Review - Page 715: a

Answer

True

Work Step by Step

We have $(f *g)(t)=\int^t_0 f(t- \tau)g(\tau) d\tau\\ (g*f)(t)=\int^t_0 g(t-\tau)f(\tau) d\tau$ We can notice that if we substitute $u=t-\tau$ to $(g*f)(t)=\int^t_0 g(t-\tau)f(\tau) d\tau$ then the equation will become $(f *g)(t)=\int^t_0 f(t- \tau)g(\tau) d\tau$. Hence, it is true to say that $f*g=g*f$
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