- #1

- 166

- 1

To write down the equation

$$ z(t) = - y(t) + \tau \frac{\partial y}{\partial t} $$ the following notation is employed

$$ z(t) = -(1-\tau \frac{\partial }{\partial t}) y $$

So far so gud. But then, the following happens

$$ \frac{ z(t)}{1-\tau \frac{\partial }{\partial t}} = - y $$

I am not making much sense of this.

The author continues by noting that

$$\frac{ 1}{1-\tau \frac{\partial }{\partial t}} \approx 1 + \tau \frac{\partial }{\partial t}$$

which moves the time derivative to the function z.

I am unsure on the procedure, considering operators as objects on which even division works, can anybody shed any light?

Many thanks