Math 302: Applications and Numerical Solution of Ordinary Differential Equations

http://www4.ncsu.edu/eos/users/w/white/www/white/ma302/ma302hp.htm

NCSU Statement on Disability and Honesty

Instructor: Robert E. White, Spring 2008

This course uses Matlab, Matlab's ODE suite, and is taught at a level suitable for students who have passed two semesters of calculus. There are five parts, and each has three lectures. The first lecture introduces a new topic, and the following two lectures will stress applications and variation of the model's parameters.  Additional course materials can be found in the texts by Danby, or Nagle, Saff and Snider.

Grading and This Week's Work Grades for section 001, 002
Sample Report
Matlab m-Files

Part I: First Order ODE and Euler Methods

1. Matlab (plot, function, loop, m-files), y(t) = 70 +130e^-kt
2. Newton's law of cooling, error = O(1), Euler
3. Falling mass, error = O(2), improved Euler

Part II: Higher Order Methods

4. LR circuit, variable step size
5. Heating, Taylor method with error = O(4);
6. Population, Runge-Kutta methods

Part III: Logistic ODE and Systems

7. Population with harvesting, ODE45
8. Spread of information, ODE45

9. Predator-prey, ODE45

Part IV: Higher Order Systems

10. Predator and two prey, ODE45
11. Mass-spring and resonance, ODE45
12. LRC circuit and tuning, ODE45

Part V: Stiff Systems

13. Rapid cooling, Euler-trapezoid, ODE23s
14. Van der Pol circuits, ODE23s
15. Oregonator chemical reactions, ODE15s