Let the initial voltages on the capacitors be represented as voltage sources in series with the capacitors and the initial currents through the inductors be represented as current sources in parallel with the inductors

Relationship between branch and loop currents

1. Augmented( incidence matrix of a directed graph nodes(N+1), branches(B)

We define transfer function H(s) as a ratio of the Laplace transform of system output (or response)(s) to the Laplace transform of the input(or forcing function)v(s) when all initial conditions are zero, then

15-6 The partial-fraction-expansion method

15-4 Laplace transform of some simple time function 1. The unit step function

We define the unit impulse as a function of time which is zero when its argument, generally (t-o), is less than zero; which is also zero when argument is greater than zero; which is infinite when its argument is zero; and which has unit area

14-8 Definition of the Fourier transform The exponential form of the Fourier series

14-6 Effective values and power The effective or rms value of the function f(t) is

14-4 Line spectrum A plot showing each of harmonic amplitudes in the wave is called the line spectrum