Hi, Everyone. I am new to electronics in general so I have a rather uninformed question. It seems that a lot of circuits out there are presented "as is" without necessary mathematical calculations. When I took my physics, we were taught KCL, KVL, RLC etc. I enjoy deriving circuit behavior using math alone. The other day I verified LC tank voltage solve second-order ODE :) For example, the other day I looked at this circuit: http://www.uoguelph.ca/~antoon/circ/555dcac.html. Is it possible using calculus, differential equations and other math/electronics rules to describe why the square (pulse) output of the IC555 will be smoothened into sine wave by C4 and L1 ? Also, is there a general FREE software that I could use for comprehensive circuit simulation, so that mathematical expressions behind circuit function are shown? Thanks to all.