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:

• Craig office hours: Tuesday, 12/4, 2:45-3:15pm, SH 6507

• Craig office hours: Thursday, 11/6, 11-11:30am, SH 6507

• Craig section: Wednesday, 12/12, 3-4pm, SH 4607

• Wells office hours: Wednesday, 12/12, 3:45-4:45pm, Math Lab

• Craig office hours: Tuesday, 12/4, 2:45-3:15pm, SH 6507

• Craig office hours: Thursday, 11/6, 11-11:30am, SH 6507

• Craig section: Wednesday, 12/12, 3-4pm, SH 4607

• Wells office hours: Wednesday, 12/12, 3:45-4:45pm, Math Lab

** 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.)

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** Supplemental References:**

Nonlinear Dynamics and Chaos, Strogatz

Differential Equations and Dynamical Systems, Perko

** 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 SOL3 | LEC6 | |

7 | Oct 18 (Th) | classification of planar systems | 4.1 | LEC7 | |

8 | Oct 23 (T) | first midterm, over lectures 1-7 |
Mid1 Mid1SOL | PracMid1 PMid1SOL | |

9 | Oct 25 (Th) | planar sys: rep evalues/changing coord | 3.3-3.4 | LEC8 | |

10 | Oct 30 (T) | linear algebra review, matrix exponential | 5.3-5.5, 6.4 | HW4 SOL4 | LEC9 |

11 | Nov 1 (Th) | higher dim'l linear sys, part one | 6.1-6.3 | LEC10 | |

12 | Nov 6 (T) | higher dim'l linear sys, part two | HW5 SOL5 | LEC11 | |

13 | Nov 8 (Th) | examples of higher dim'l linear sys | LEC12 | ||

14 | Nov 13 (T) | second midterm, over lectures 8-13 |
Mid2 Mid2SOL | PracMid2 PracMid2SOL | |

15 | Nov 15 (Th) | stable, unstable, and center subspaces | LEC13 | ||

16 | Nov 20 (T) | existence/uniqueness | 7.1-7.3 | HW6 HW6tex | LEC14 |

17 | Nov 27 (T) | examples of nonlinear systems | 8.1 | HW7 HW7tex | LEC15 |

18 | Nov 29 (Th) | sinks, sources, and saddles | 8.2-8.3 | LEC16 | |

19 | Dec 4 (T) | stability and bifurcations | 8.4-8.5 | HW8 HW8tex | LEC17 |

20 | Dec 6 (Th) | review and math movie competition | LEC18 | ||

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

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