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Ordinary Differential Equations

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About the Tutorial:

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.   

 

About the Instructor(s):

Elizabeth Bradley is Professor of Computer Science at the University of Colorado, Boulder and External Professor at the Santa Fe Institute.

Elizabeth Bradley did her undergraduate and graduate work at MIT, interrupted by a one-year leave of absence to row in the 1988 Olympic Games, and has been with the Department of Computer Science at the University of Colorado at Boulder since January of 1993.  Her research interests include nonlinear dynamics, artificial intelligence, and control theory.  She is the recipient of a NSF National Young Investigator award, a Packard Fellowship, a Radcliffe Fellowship, and the 1999 student-voted University of Colorado College of Engineering teaching award.

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Prerequisites:

Calculus

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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