This section deals with finding the factors of equations of the form:

Y=C₁+C₂*X+C₂*X²+...+C_n*X^{n  (where C}₁^{, C}₂^,...,C_n ^{are constants)}

and one simple program for evaluating polynomials with sin/cos terms.  Bairstow’s method finds both real and imaginary roots!

To download programs, please go to one of these pages:

Real Roots of Polynomials: Half Interval Search

Real Roots of Polynomials: Newton’s Method

Roots of Polynomials: Bairstow’s Method

Roots of a Trigonometric Polynomial

An aside:

Classical Solution Methods for Linear Differential Equations (a PDF file)

This excerpt is from “System Dynamics: Modeling and Resonse,” by Ernest O. Doebelin, 1972 (no longer in print). Professor Doebelin taught at The Ohio State University, and was a terrific teacher.  His techniques were practical and constructive.  For example, in the link above, you’ll find the following quote:

“No matter what method one might propose, a mathematician can always concoct a sufficiently "pathological" f(t) to thwart it. Thus, one must be satisfied with methods which handle a certain class of function.”

Armed with Bairstow’s method for solving polynomials, anyone that can do some algebra, can also solve linear differential equations and perform some fairly sophisticated engineering modeling.  It ain’t hard - some “teachers” just try to make it look difficult!.