I'm a second year Electrical Engineering student, and my lecturer recently introduced some concepts which I haven't been exposed to before relating to the Laplace transform (the course is on the frequency response of circuits). I've only got a superficial understanding of Laplace transforms.
My main question is there appears to be some ability to use the Laplace transform of a function to break it into transient and steady-state parts. How is this?
Also, when I learned Laplace transforms, we didn't discuss what 's' actually is. What is it? Apparently it's some complex number (sigma + omega * i) and, when we're concerned with the steady-state response, it equals (omega*i). What is going on here?
I'm guessing I'm not coming across clearly - that's because I don't really know where to start. I'm a bit lost. If someone could clarify the topic in general (frequency response of circuits, with particular reference to Laplace transforms and representation in the Laplace domain), that would be awesome.
I'm more than happy with being pointed to good reference material rather than being told the answers. If it's a simple explanation though, it'd be nice to be handed it straight-up in an answer.
Thanks in advance for your help.