Differential Equations

CAS MA 226, Fall 2007

MWF 2-3 in CAS 116

Phone: 617 358 4684
E-mail: pnorbury bu edu
Office Hrs: W 10-12, F 9-10

Homework problems from Blanchard, Devaney & Hall.
Due Wednesday before class. Hand in only even number problems.
  1. Due Sep 12: 1.1: 1,2,3,4,6,7,10,11,12,15,16,19,20
    Interpret the centre/focal point of the F versus R graph in the PredatorPrey model using the software Differential Equations.
  2. Due Sep 19: 1.2: 1-6, 27-31 1.3 1,4,5,7,9,12,15,22 1.4 4,5,14
  3. Due Sep 26: 1.5 5-9, 13 1.6 1,4,7,10,11,16,19,22,23,26
  4. Due Oct 10: 1.7 3,5,6,22 1.8 3,4,5,21-23,30 3.1 5,10,14,17 2.1 23,25 2.2 10,21
  5. Due Oct 17: 2.3 5,6,7,11,12 2.4 3,4,7,8 3.1 25-28
  6. Due Oct 24: 3.2 3,4,12,20 3.3 5,6,19-24
  7. Due Nov 7: 3.4 1-4,9,11,12,15,23 3.5 1,4,5,8 3.6 3,5,6,7,8
  8. Due Nov 14: 3.6 19,20,27,28 3.7 1,2,8,12
  9. Due Nov 28: 4.1 1,3,8,13,16,19,24,33,34 4.2 13,14,17 4.3 11,12,18,21,24
  10. Due Dec 5: 5.1 1,2,7,8,18,26 6.1 7,9,16
Handouts Print out before each class and bring to class.
  1. December 10, 2007 Notetaker helper
  2. December 7, 2007 Notetaker helper
  3. December 5, 2007 Notetaker helper
  4. December 3, 2007 Notetaker helper
  5. November 30, 2007 Notetaker helper
  6. November 28, 2007 Notetaker helper
  7. November 26, 2007 Notetaker helper
  8. November 19, 2007 Notetaker helper
  9. November 14, 2007 Notetaker helper
  10. November 9, 2007 Notetaker helper
  11. November 7, 2007 Notetaker helper
  12. November 5, 2007 Notetaker helper
  13. November 2, 2007 Notetaker helper
  14. October 29, 2007 Notetaker helper
  15. October 26, 2007 Notetaker helper
  16. October 24, 2007 Notetaker helper
  17. October 22, 2007 Notetaker helper
  18. October 19, 2007 Notetaker helper
  19. October 17, 2007 Notetaker helper
  20. October 12, 2007 Notetaker helper
    Euler system
    Euler predator-prey
  21. October 10, 2007 Notetaker helper
  22. October 9, 2007 Notetaker helper
  23. October 5, 2007 Notetaker helper
  24. October 1, 2007 Notetaker helper
  25. September 28, 2007 Notetaker helper
  26. September 26, 2007 Notetaker helper
  27. September 24, 2007 Notetaker helper
  28. September 21, 2007 Notetaker helper
    Quicktime phase line animation
  29. September 19, 2007 Notetaker helper
  30. September 17, 2007 Notetaker helper
    Euler's method Euler's method with varying step-size Euler's method difficulty
  31. September 14, 2007 Notetaker helper
  32. September 12, 2007 Notetaker helper
  33. September 10, 2007 Notetaker helper
  34. September 7, 2007 Notetaker helper
  35. September 5, 2007 Notetaker helper
Solutions to first midterm

Solutions to second midterm

Projects

  1. Due Oct 17: Project 1 The glider p.556 from Blanchard, Devaney & Hall
  2. Due Nov 30: Project 2 The forced pendulum

Text

Differential Equations (third edition) Paul Blanchard, Robert L Devaney, Glen R Hall
Brooks/Cole Publishing Company, 2006. ISBN number 0-495-01265-3

Course content

In this course we will analyse differential equations qualitatively, analytically and numerically. Throughout the course we will use mathematical software to analyse and visualise differential equations and their solutions. Computers are a powerful tool that enhance the way we learn material. With computers we can numerically/approximately solve any differential equation. This gives us an immediate understanding of the problem and enables better mathematical analysis.

We begin the course with simple systems that demonstrate the definition of a differential equation and the qualitative, analytic and numerical approaches. We then do a systematic study of first order linear systems. Next we study non-linear systems which give more real-life examples, applying some ideas from the linear case. We also introduce the Laplace transform which is a powerful tool for the study of differential equations.

Assessment:

Homework will be assigned each lecture and due before the lecture on the Wednesday in the following week. A copy of what is assigned will appear on the web. It will be good practice to complete a portion of the assignment after the corresponding lecture. Please staple your homework. Late homeworks will not be accepted without medical evidence. You are permitted and encouraged to consult with other students on homework problems, but this should be done on a general level of finding the solution of a problem. The final writeup of a problem set must be done by each student individually. There will be two projects which you will do in groups of 3 or 4. They will be due before class on October 17 and November 30. The midterm exams will be October 3 and October 31, and the last exam will be December 12. No makeups for exams will be given, and exams will not be excused without medical evidence. Students should abide by the CAS academic conduct code.