with properly selected components, this simple passive differentiator can beat the performance of an op-amp differentiator
http://www.e-insite.net/ednmag/archives/1994/042894/09di2.htm
http://www.ifwtech.demon.co.uk/g3sek/tr-bias/tr-bias1.htm
aimed at beginners
http://members.tripod.com/~schematics/index.html
use computer and ink jet printer for nice front panels.
http://www.aade.com/sexypnls.htm
http://www.techlearner.com/Semiconductors.htm
There is no single PID algorithm. Different fields using feedback control have probably used different algorithms ever since math was introduced to feedback control.
http://members.aol.com/pidcontrol/pid_algorithm.html
Shows the standard 3-band method for the commonest E12 values.
http://www.4qdtec.com/colcode.html
http://www.gbonline.com/~multiplx/wireless/pdf/julaug1998-p64.pdf