Math 119a: ODEs & Dynamical Systems

**Professor:** Katy Craig, SH 6507, katy•craig•math at gmail • com

**Teaching Assistant:** Sarah Wells, SH 6431B, swells at math • ucsb • edu

** Lecture/Section/Office Hours:** Attendance in lecture is mandatory. Students who do not attend lecture may be unenrolled in order to admit students who do attend lecture. Attendance in section is optional.

** Class calendar: **

Schedule change: on Wednesdays, October 10th and 24th Sarah's office hours will be from 1-2PM.

** Textbook:** Differential Equations, Dynamical Systems, & an Introduction to Chaos, Hirsch, Smale, & Devaney

Any edition of the above textbook is fine. It is easier to read mathematics on paper, and I strongly recommend that you buy a hard copy of some edition. (Used versions of the second edition can be purchased for ~$35.)

** Supplemental Reference:** Nonlinear Dynamics and Chaos, Strogatz

** Exams:** There will be two midterms and one final exam. The examinations will be closed book and closed note. There will be no retaking or rescheduling of exams under any circumstances, as the grading scheme allows you to drop your lowest midterm score.

** First Midterm:** Tuesday, October 23rd, 3:30-4:45PM

** Second Midterm:** Tuesday, November 13th, 3:30-4:45PM

** Final Exam:** Thursday, December 13th, 4:00-7:00PM

**Homework:**

• Homework assignments will be posted on this website and collected during lecture.

• Only problems marked with an asterisk (*) should be submitted for grading.

• At least one problem on each of the exams will be chosen from the non-asterisked homework problems.

• No late homework will be accepted.

• Homework 1, 2, and 3 will be used as a measure of class attendance and must be turned in.

• The lowest two homework grades will be dropped and will not count toward the final grade.

** Grading Scheme:** homework: 10%, highest midterm score: 40%, final: 50%

If you have questions about the grading of any assignment or exam, you have one week after it is handed back to request a regrade.

** Prerequisites:** Math 8

** Outline of Course: **

Part I: Linear Systems | Part II: Nonlinear Systems |
---|---|

planar systems | existence & uniqueness |

linear algebra review | sinks, sources, and saddles |

classification of planar systems | stability and bifurcations |

higher dimensional linear systems & matrix exponential |

topic | reading | due today | notes/review materials | ||
---|---|---|---|---|---|

1 | Sept 27 (Th) | logistic equation and bifurcations | 1.1-1.3 | LEC1 | |

2 | Oct 2 (T) | def'n of planar linear systems | 2.1-2.4 | HW1 SOL1 | LEC2 |

3 | Oct 4 (Th) | solving lin systems, lin algebra review | 2.5-2.7, 5.1-5.2 | LEC3 | |

4 | Oct 9 (T) | planar sys: real, distinct evalues | 3.1 | HW2 SOL2 | LEC4 |

5 | Oct 11 (Th) | planar sys: complex evalues (I) | 3.2 | LEC5 | |

6 | Oct 16 (T) | planar sys: complex evalues (II) | HW3 HW3tex | LEC6 | |

7 | Oct 18 (Th) | planar sys: repeated evalues | 3.3 | ||

8 | Oct 23 (T) | first midterm, over lectures 1-7 |
|||

9 | Oct 25 (Th) | linear algebra review | 5.3-5.5 | ||

10 | Oct 30 (T) | classification of planar systems | 4.1-4.2 | ||

11 | Nov 1 (Th) | higher dim'l linear sys: distinct evals | 6.1-6.2 | ||

12 | Nov 6 (T) | higher dim'l linear sys: repeated evals | 6.3 | ||

13 | Nov 8 (Th) | matrix exponential | 6.4 | ||

14 | Nov 13 (T) | second midterm, over lectures 8-13 |
12 | ||

15 | Nov 15 (Th) | nonlinear sys: existence/uniqueness | 7.1-7.3 | ||

16 | Nov 20 (T) | examples of nonlinear systems | 8.1 | ||

17 | Nov 27 (T) | sinks, sources, and saddles | 8.2-8.3 | ||

18 | Nov 29 (Th) | stability and bifurcations | 8.4-8.5 | ||

19 | Dec 4 (T) | catch up | |||

20 | Dec 6 (Th) | review and math movie competition | |||

Dec 13 (Th) | final exam, 4:00-7:00PM |

As an opportunity for extra credit, we will hold a math movie competition. The goal is to make the best math movie, lasting three minutes or less. Submissions are due on Thursday, November 29th. The winner of the competition will receive ten points of extra credit on their final exam. Second place will receive five points of extra credit, and third place will receive three points of extra credit.

Submissions should be uploaded to YouTube, Vimeo, or a similar site. Links to the movies can be emailed to me. (Please do not send the movies as email attachments.)

Potential topic ideas for inspiration...

• The dynamics of fractals

• Order in chaos

• Synchronization and periodicity in biology

• The mathematics of opinion dynamics

• Mathematical models of disease