This book is written based on my M. Sc. Engineering thesis. The method uses a set of closed loop transfer functions, one for each synchronous machine and derived by taking Laplace transformation of the machine's nonlinear swing equation in a tricky way. The transfer function directly takes into account the time of fault clearing and the changes in the maximum electrical power output of the machine due to changes in the prefault network topology during and after clearing the fault. The earliest possible location of the root of the characteristic equation (the denominator of the transfer function equated to zero) is searched in the s-plane for each machine starting from a real value of s which is the same for all the machines. The narrowest possible range i. e the lower and upper limits of the location is found by observing sign changes of the transfer function expression evaluated at several step values of s obtained by increasing starting value by a suitable chosen increment.