Laplace Transform, Transfer Function, Characteristic Equation, DC Gain

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Convolution

The definition of convolution is total pain.

Laplace transform

Final value theorem, Laplace transform/inverse transform

Transfer function

Since it’s hard to generate a precise impulse function with real equipment, taking the Laplace transform of the impulse response is difficult in practice.

So it’s better to define the transfer function as output/input: G(s) = Y(s)/U(s)

y(t) in the time domain

For y(t) in the time domain, it’s simplest to use the inverse Laplace transform.

Characteristic equation, DC gain