Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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12 In Sync



To capture the notion of rates of change that can themselves change, we need the concept of a derivative.

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Differential Calculus

First described rigorously by Newton and Leibniz, differential calculus is the mathematics of changing quantities.

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Differential Equation

A differential equation is an expression that relates quantities and their rates of change. The solution to a differential equation is not simply a number; it is a function.

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Non-Constant Slope

A non-constant slope describes a rate of change that itself can change.

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An oscillator is a function that varies between two values.

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The slope-intercept form of a linear equation is a common way to represent the mathematics of change. An example of this concern with relationships is the familiar slope-intercept form of the equation of a line: y = mx +b.


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Spontaneous Synchronization

Spontaneous synchronization is a special case of complicated dynamic phenomena. Understanding the mathematics of how, and under what circumstances, entities can come into synchronization with one another provides a starting point for exploring the vast world of nonlinear dynamics.

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The Kuramoto Model

The Kuramoto Model describes large systems of coupled oscillators.

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