Professionals in mathematics and physics view linear equations as simple. A nonlinear equation forms an S-curve, bell curve or another nonlinear shape on a graph. On the other hand, understanding concepts such as the "business cycle" involves economic and social mechanisms that are very different from the rules of the stock market. Here are some key differences between linear and nonlinear equations: A linear equation forms a straight line on a graph. Indeed, in the stock market, the rules are specifically designed to make prediction impossible or at least very difficult. The theory for solving linear equations is very well developed because. " For in stance, in mathematically modelling the stock market, uncertainty is a prime and indispensable component of a model. In math and physics, linear generally means simple and non-linear means complicated.
The course deals with existence uniqueness, and analyses in the phase space. The inherent lack of precise knowledge in the social sciences is a fun damental trait that must be distinguished from "uncertainty. Nonlinear Differential Equations Teaching semester. The reach of such analysis extends far beyond tech nical clarifications of classical theories that were generally expressed in imprecise literary prose. Nevertheless, as may be inferred from a study of the models discussed in this book, the qualitative analysis of deterministic models has an important role to play in understanding the fundamental mechanisms behind social sci ence phenomena.
Con sequently, a deterministic model is rarely expected to yield a precise description of the actual phenomenon being modelled. Social science phe nomena typically defy precise measurements or data collection that are comparable in accuracy and detail to those in the natural sciences. It is generally acknowledged that deterministic formulations of dy namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences.
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