Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
To capture the notion of rates of change that can themselves change, we need the concept of a derivative.
First described rigorously by Newton and Leibniz, differential calculus is the mathematics of changing quantities.
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.
A non-constant slope describes a rate of change that itself can change.
An oscillator is a function that varies between two values.
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.
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.
The Kuramoto Model describes large systems of coupled oscillators.