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Differential equations: course

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Book

Planned for Fall 2011.

1 Description

This is a one-semester course in differential equations and applications.

2 Prerequisites

3 Outline

As far as modeling, here's what I have in mind. Typically, this is how things go in such a course:

 model -> derivation of the DE -> analysis -> discretization -> difference equation -> 
 -> simulation -> analysis etc. 

I would like to start with discrete differential forms (you can see some of it here: Discrete exterior calculus). Then instead of DEs, one will deal with "discrete differential form equation" (I don't know a better name yet). Those are something like a more sophisticated version of cellular automata. Then this how it will go:

 model -> derivation of the discrete differential form equation -> simulation -> 
 -> analysis -> continuous differential form equation (same!) -> DE -> analysis etc. 

The modeling will be done with Excel.

Topics:

  • Review of calculus
  • First-order ordinary differential equations
  • Second-order ordinary differential equations
  • Differential forms
  • Applications: vibrations and electrical circuits
  • Laplace transform, approximate solutions, orthogonal functions
  • Fourier series
  • Partial differential equations: heat, wave, and Laplace equations


4 Notes

5 Further reading