Ordinary Differential Equations

Overview

This tutorial contains excerpts from Elizabeth Bradley’s Nonlinear Dynamics course.  Note that Complexity Explorer tutorials are meant to introduce students to various important techniques and to provide illustrations of their application in complex systems.  A given tutorial is not meant to offer complete coverage of its topic or substitute for an entire course on that topic.   

This tutorial is designed for more advanced math students who have taken Calculus.   

Syllabus

1. Ordinary Differential Equations (Liz Bradley)
2. Nonlinearity and nonintegrability
3. ODEs, vector fields, and dynamical landscapes
4. Introduction to ODE Solvers
5. Forward and Backward Euler
6. Solving Simple Harmonic Oscillator ODEs
7. ODE Solvers: Error and Adaptation
8. Production ODE Solvers
9. Numerical Dynamics
10. Unit 3 Homework