# Math 123: Ordinary Differential Equations

## UC Berkeley, Spring semester 2016.

**Lectures:** TTh 3:30 -- 5:00. Lectures are in 241 Cory Hall.

**Office Hours:** T 5:00 -- 6:30, W 4:00 -- 5:30. Additional office hours by appointment.

**Textbook:** We will primarily follow "The Qualitative Theory of Differential Equations" by Brauer and Nohel. Suggested resources for additional and supplemental topics will be posted as needed.

**Prerequisites:** Ideally Math 54 and 104 or equivalent courses. Contact me if you have questions about your preparedness.

**Course outline: **The course will consist of

- Review: techniques and tricks. Motivation
- Existence and uniqueness theory
- Theory of linear systems
- Stability theory, Lyapunov's method
- Applications and additional topics as time permits, e.g. the Liénard equation, the Poincaré-Bendixon theorem, numerical methods.

See here for a list of class policies, including the grading scheme. Familiarizing yourself with these policies is part of the expectations of this course. An approximate schedule, to be updated as the course progresses, is here.

**Homework:** Homework is due at the beginning of each Thursday lecture. See the list of class policies for further details regarding homework.

- Homework 1. Due Thursday, January 28 at the beginning of class.
- Homework 2. Due Thursday, February 4 at the beginning of class.
**Updated**for clarification on Feb. 1. - Homework 3. Due Thursday, February 11 at the beginning of class.
- Homework 4. Due Thursday, February 18 at the beginning of class.
**Updated**on Feb. 17. - Homework 5. Due Thursday, February 25 at the beginning of class.
- Gap week due to midterm examination.
- Homework 6. Due Thursday, March 10 at the beginning of class.
- Homework 7. Due Thursday, March 17 at the beginning of class.
**Updated**on Mar. 15. - Homework 8. Due Thursday, March 31 at the beginning of class.
- Homework 9. Due Thursday, April 7 at the beginning of class.
- Homework 10. Due Tuesday, April 19 at the beginning of class.
**Note**altered due date. - Homework 11. Due Tuesday, April 26 at the beginning of class.
**Note**altered due date. - Homework 12.
**Not**to be handed in.**Updated**on Apr. 27.

**Final Exam: **Friday, May 13th, 7-10PM in 241 Cory Hall.

**RRR Week:** I will be away, so there will be no office hours. Feel free to email me questions -- I encourage you to carefully write the question by hand and send a photo, as this is often easier (and clearer) for both of us.

**Office hours during finals week:** Tuesday, May 10, 11:30--1:00. Wednesday, May 11, 11:30--1:00.