Nonlinear Dynamics and Chaos – Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz’s book, “Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.”

The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.

The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.

Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics

Selections from Science and Sanity represents Alfred Korzybski’s authorized abridgement of his magnum opus, Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. This second edition, published in response to the recent Korzybski revival, adds new introductory material and a revised index, providing an accessible introduction to Korzybski’s arguments concerning the need for a non-Aristotelian approach to knowledge, thought, perception, and language, to coincide with our non-Newtonian physics and non-Euclidean geometries, to Korzybski’s practical philosophy, applied psychology, pragmatics of human communication, and educational program. Selections from Science and Sanity serves as an excellent introduction to general semantics as a system intended to aid the individual’s adjustment to reality, enhance intellectual and creative activities, and alleviate the many social ills that have plagued humanity throughout our history.