A previous volume, Stochastic Systems (1983), was the first systematic book bringing nonlinear and stochastic equations within the reach of engineers and physicists concerned with the difficulties of real systems and frontier 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 engineering. Previously, either such problems were not realistically formulated or the approximations made and the methods used made the results either unrealistic or misleading. This work will necessitate the rewriting of the mathematics 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.