Math 123: Ordinary Differential Equations
Section 1 (24090), Fall 2018

Wednesdays 11:30 AM - 1:00 PM, Thursdays 11:00 AM - 12:30 PM (in 1071 Evans) and by appointment. At other times I will be answering questions on Piazza.

Text

Required: Morris W. Hirsch, Stephen Smale, and Robert L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Academic Press/Elsevier, third edition, 2013, Hardcover ISBN: 9780123820105, eBook ISBN: 9780123820112

Other useful books:

Steven H. Strogatz, Nonlinear Dynamics and Chaos, Westview, 1994
James D. Meiss, Differential Dynamical Systems, SIAM, 2007
Lawrence Perko, Differential Equations and Dynamical Systems, third edition, Springer Text in Applied Math. 7, 2001

Syllabus

The (ambitious) plan is to cover Chapters 1-10, 12, 13 and/or 14, and 17 of Hirsch-Smale-Devaney.

Linear systems. Classification of planar linear systems. Existence and uniqueness theorem for solutions of ODEs. Dependence on initial conditions. Equilibria in nonlinear systems. The Hartman-Grobman theorem. Stability of equilibria. Gradient systems. Hamiltonian systems. Closed orbits and the Poincaré-Bendixson theorem. Applications in circuit theory and classical mechanics. The Lorenz system.

Each week I will assign the reading for the following week, which you are required to do ahead of class. You are welcome to supplement your reading by looking at other sources such as the books recommended above.

#	Week of	Reading
1	8/23	Chapter 1
2	8/27	Chapter 2

Exams

There will be one in-class midterm and a final exam. The exam schedule:

Midterm: Thursday, October 18

Final exam: Tuesday, December 11, 8:00-11:00 AM

No make-up exams will be given.

Disabled students requiring accommodations should contact the Disabled Students' Program.

Grading policy

The final grade will consist of four components:

Homework 30%

Midterm 30%

Final 40%.

Each of the above three grades will be curved into a number on a consistent scale.

Your midterm grade will be replaced by the curved final exam grade if the latter is higher.

The three curved grades will be added up and converted into a final course grade.

Curving means that the difficulty of exams does not affect your grade: if an exam is extremely difficult (highly unlikely), then a lower score will be sufficient to get an A, while if an exam is very easy (also unlikely), you might need a very high score to get an A. After each midterm you will be given the letter grade cutoffs.

Please note: incomplete grades, according to university policy, can be given only if unantipicated events beyond your control (e.g. a medical emergency) make it impossible for you to complete the course, and if you are otherwise passing (with a C or above).

Handouts

None yet.

Homework

There will be weekly homework assignments. You are welcome to work on the homework collaboratively but I expect you to write your solutions in your own words. I also encourage you to discuss homework questions on Piazza.

#	Due date	Assignment
1	8/30	Chapter 1, exercises 5, 8, 9, 11, 12, 13, 14, 15

Piazza

To handle questions posed outside of class, we will be using Piazza, a free platform for instructors and GSIs to efficiently manage out-of-class Q&A. On the class dashboard, students can post questions and collaborate Wikipedia-style to edit responses to these questions. Instructors can also answer questions, endorse student answers, and edit or delete any posted content. Instead of emailing me math questions, I encourage you to post them to Piazza. One of many great things about Piazza is that it supports LaTeX.

Each student will be invited to join Piazza by email. Please join it as soon as you can, as I plan to use Piazza extensively. I will not be using bCourses.

Instead of sending me email, please create a post on Piazza with your question or concern. Private or anonymous post are fine, though they should be used rarely.

Top answerers on Piazza will receive extra credit.

Last modified: Tue Sep 4 13:07:43 PDT 2018

Math 123: Ordinary Differential Equations Section 1 (24090), Fall 2018

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