I am doing laplace transform in a class and I hate how there seems to be no graphical support when things are transformed to laplace domain i.e. nobody cares what they look like in laplace domain
But I think I have found a short cut, prove me wrong!
Take the laplace transform of y(t) = 1 yields Y(s) = 1/s
Cheat and plot it as a function of real number
Now I rotate this graph around the z-axis and get a volcano looking thing
Voilà, wolfram alpha seems to approve
Can anyone opine on whatever little mathematic may be in this approach? Is this method extendable to other functions of complex variable?
This seems to have little mathematical basis but I wonder if I can fight with other laplace transforms (usually rational functions of the form p(s)/q(s)) using similar method and attempt to "visualize" what they might look like in complex domain