List of all pages
- Equilibria in discrete dynamical systems
An introduction to the concept of equilibria in discrete dynamical systems and how to calculate them. - The stability of equilibria for discrete dynamical systems
Identifying stable and unstable equilibria though the derivative of the updating function. - Examples of determining the stability of equilibria for discrete dynamical systems
Examples demonstrating how to calculate the stability of equilibira analytically from the derivative of the updating function. - The idea of stability of equilibria for discrete dynamical systems
An introduction to the concept of stable and unstable equilibria and how to use cobwebbing to identify stability. - Definition: Equilibrium definition
An equilibrium of a dynamical system is a value of the state variables where the state variables do not change. This means if the systems starts at an equilibrium, the state will remain at the equilibrium forever. - Evidence for additional structure in real networks
Real networks seems to have additional structure than that captured by a random network with independent edges. - Exploring the derivative of the exponential function
A guided tour into the reasons that the derivative of the exponential function with base e is the function itself. - The exponential function
Overview of the exponential function and a few of its properties. - Exponential growth and decay modeled by continuous dynamical systems
Overview of exponential growth and decay in continuous time, modeled by a linear autonomous differential equation. - Exponential growth and decay: a differential equation
Solving a differential equation to find an unknown exponential function. - Exponential growth and decay modeled by discrete dynamical systems
Overview of exponential growth and decay in discrete time. Exploration of their qualitative properties as well as solutions to the dynamical system. - Discrete exponential growth and decay exercise answers
Answers to selected exercises on solving problems involving exponential growth and decay in discrete time. - Discrete exponential growth and decay exercises
Exercises on solving problems involving exponential growth and decay in discrete time. - Basic rules for exponentiation
A brief overview of the basic rules for exponents or powers. - For-loops in R
How to use a for-loop in R - Forming plane examples
Examples showing how to determine the equation of a plane. - Forming planes
A description of ways to specify a plane. Interactive graphics illustrate the concepts. - The Forward Euler algorithm for solving an autonomous differential equation
Using the linear approximation, or tangent line, to the solution of a differential equation to estimate the solution over small intervals. - From discrete dynamical systems to continuous dynamical systems
Illustration of how a discrete dynamical system approaches a continuous dynamical as the size of the time step shrinks. - Definition: Function definition
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
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