By R. Cody, J. Smith
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Extra resources for Applied Statistics and the SAS Pgmg Lang.
However, computers have not eliminated the problem of choosing between accuracy and speed; they have only shifted the break-even point to a higher level. We would like to suggest two particular areas of concern which we feel should be reviewed from time to time by every analyst. The first is to maintain an awareness of the limitations of any mathematical model resulting from the various approximations imposed during the modeling process. This is very important in order to avoid predicting the behavior of a system by a solution obtained from a model based on postulates which are invalid in the region of interest.
This expansion will contain powers of z – z0 with negative exponents, for otherwise z = z0 would not be a singular point. Hence we have There are two possibilities: a. 1) has only a finite number of powers of z – z0 with negative exponents. In this case w(z) is said to have a pole at z = z0. If m is the largest of the negative exponents and if the function behaves regularly (is analytic) and is not zero at the point z0, m is called the order of the pole z0 and w(z) is said to have a pole of the mth order at the point z0.
N is the number of zeros and P the number of poles lying within the contour C. Each zero and pole must be counted in accordance with its multiplicity. In recent years this theorem has been applied extensively to the study of the stability of electrical and mechanical dynamical systems. In order that these systems shall be stable, it is necessary that their characteristic equations have roots whose real parts are negative (see Chap. 6). The above theorem provides a method of determining whether the roots of characteristic equations have positive real parts without solving the equations.
Applied Statistics and the SAS Pgmg Lang. by R. Cody, J. Smith