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A previous volume, Stochastic Systems (1983), was the first systematic
book bringing nonlinear and stochastic equations within the reach of engi
neers and physicists concerned with the difficulties of real systems and fron
tier problems in which conventional techniques such as linearization and
perturbation are not sufficient or realistic.
This volume increases very substantially the scope of the work to cover
very wide classes of equations. It is a simple and powerful method applicable
to the solution of a multitude of problems in physics, engineering, operations
research, systems analysis, economics, biology, medicine, and other fields.
Forthcoming volumes will deal with applications to physics and engineer
ing. Previously, either such problems were not realistically formulated or the
approximations made and the methods used made the results either unreal
istic or misleading. This work will necessitate the rewriting of the mathemat
ics and physics books since mathematics deals largely with linear operator
theory and physics with perturbation. In my view, this overall work will have
a profound impact on mathematics and on the modeling of problems of
physics, engineering, economics, biology, and medicine and may well be
viewed in retrospect as one of the significant contributions of this century.
This work is a scientific breakthrough. The importance of it cannot be
overemphasized.
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