MAT335H1 Lecture Notes - Lecture 1: Exponential Growth, Stamen, Chaos Theory

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2 Dec 2015
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The aim of the rst few lectures was to present a brief history of the subject chaos theory. Here we focus on a shift of point of view in studying dynamical systems. Dynamical systems into two distinct periods: from galileo (late 1500s) to early 1800s, this period we shall call. Newtonian era, and then the period of mid 1800 to 1913 (lifetime of henry poincare, and birth of topology). There is also a third period 1960 to modern times, which is the age of computers and the impact of the most developed mathematical techniques on studying the dynamical systems. ) A dynamical system is a model for describing the evolution of certain variables in time. These variables represent natural phenomena, and dynamical systems are models that capture certain laws of nature (physics, Nance, etc) and translate them into the language of mathematics. dynamical systems capture the logic of evolution of nature and as such they are heavily relied on for forecasting.

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