Laplace&Z transform is just frequency analysis of a system with a multiplication of decaying exponential. We analyse frequency with varying Laplace Exponential, which can be seen in the formula below for laplace transfrom.
From my simple aspect I can't make the theoretical connection, how inspecting frequency with decaying exponential helps with understanding how system will behave? And how it helps with coping with differential functions for example "Analysis of Electric Circuits". And even with IIR filters.
What further surprises me the things laplace&Z transforms used. They seem to me completely different .But somehow multiplying the system with decaying exponential works for them all. The only similarity I see between; for example RLC curcuits and IIR filters is; these systems are not memoryless(output depends on prev. outputs).
When I search the net I see only laplace-table's, questions etc.. I don't want to solve a problem, I want to understand the problem. If somebody can explain or direct me to a link I will be thankful.