Ordinary Differential Equations

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This tutorial contains excerpts from Elizabeth Bradley's Dynamical Systems 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.

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Ordinary Differential Equations
ODEs
Vector fields
Dynamical landscapes
Nonlinearity
Nonintegrability
ODE Solvers
Forward Euler
Backward Euler
Harmonic Oscillator ODEs

Programma

  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

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