Lecture 26 - Convolution and Transfer functions

We begin by discussing the convolution product of two functions, and go on to explore some of its properties. We then uncover the deeper significance of Laplace transforms in the study of systems modelled by linear differential equations with constant coefficients. In short, by understanding the response of such a system to a unit impulse (or equivalently, the transfer function of the system), we can predict how the system will respond to an arbitrary force!

This lecture is part of a course on differential equations (Math 207, University of Washington)

[danieldshin]

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[randyh]

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[WilliamDouglasHenry]

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[arier.]

Hello. could you explain why you replace t by (t-u), yet sin(2t) you replaced by sin(2u), rather than by sin(2(t-u))? (inside the integral, 13 minutes or so into the lecture)

[asw]

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[takasoeda]

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