Math 302, Fall 2008
Applications and Numerical Solution of Ordinary Differential Equations

http://www.math.ncsu.edu/~aszanto/MA302

 

Instructor
Dr. Agnes Szanto
Harrelson Hall 347
Tel: 515-7547
E-mail: aszanto

Meet
Th 11:20-12:10pm and 12:25-1:15pm
Harrelson Hall G108

Office Hours
Th 10:00am-11:00am
Fr 11:10am-12:10pm
or by appointment

Exam Dates, Grading and Course Policies

Course Description

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.

Matlab m-Files

Part I: First Order ODE and Euler Methods

1. Matlab (plot, function, loop, m-file
2. Falling mass, Euler and improved Euler methods s), y(t) = 70 +130e^-kt
3. Cooling with variable ambient temperature, variable time steps

Part II: Logistic ODE and Higher Order Methods

4. Population, Taylor and Runge-Kutta methods
5. Population with harvesting, ODE45
6. Spread of information, ODE45

Part III: Higher Order Systems

7. Predator-prey(s), ODE45
8. SIR Epidemic model, ODE45
9. Diffusion of Heat (discrete rod), ODE45

Part IV: Vibration and Resonance

10. Mass-spring and resonance, ODE45
11. Vibrating string  (discrete string), 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