MA 775 Ordinary Differential Equations

MA 775 Ordinary Differential Equations

Course Information

Lecturer: Ryan Goh

Email: rgoh@bu.edu
Office: CDS 423
Office Hours: Monday 10:30-11:30a (priority for MA 775);
Tuesday 1:45-3:15p (priority for another class);
Wednesday 2-3:30p;
or by appointment (please provide your availability when requesting an appointment).
Web page: http://math.bu.edu/people/rgoh/

Lectures:

Time: Tuesday, Thursday 11:00am-12:15am;
Location: IEC-B04
Textbook: No required textbook

Additional References
Here are some other references which may provide an alternative viewpoint and presentation of the course material and which you might find useful.

Teschl, G. Ordinary Differential Equations and Dynamical Systems

Chicone, C. Ordinary Differential Equations with Applications

Guckenheimer, J., Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Perko, L. Differential Equations and Dynamical Systems

Coddington, E., Levinson, N., Theory of Ordinary Differential Equations

Course Webpage: http://math.bu.edu/people/rgoh/teaching/ma775-fs23/course-page.html

Course Description:



Prequisites This course assumes you have a solid background in undergraduate analysis (say at the level of BU CAS MA 511), differential equations (at least at the level of MA 226. Some background in graduate analysis (BU CAS 711) including measure theory might be helpful in a few places but is not necessary. If you haven't taken an equivalent class to BU's MA 573, it might be useful to review topics from the books by Strogatz or Hirsch,Smale,Devaney. While we will not give proofs of all background statements, relevant concepts will be refreshed and reviewed as needed.

Overview This is a graduate level introduction to ordinary differential equations and continuous time dynamical systems. This course aims to give a broad view of the subject by emphasizing key concepts and techniques at the heart of the theory as well as to highlight the many applications of the theory. It is the goal of this course that participants obtain a solid foundational knowledge of the field in order to continue research into the area and/or to apply it to their particular field of study. A coarse overview of course topics are as follows:

Communication

Please feel free to email me or stop by office hours to discuss the course. During the work week, I aim to answer any emails received within 24 hours (most of the time sooner). During the weekend, I may not answer until Sunday evening. Finally, late night emails may not be replied to until the next day. If you email to set up a meeting outside office hours please provide your availablility in the email.

Homework

There will be assigned homework every week or two throughout this semester. Assignments will be posted on the course webpage and typically you will be given a week to complete them. Please submit all homeworks to me via email in PDF form (either scanning handwritten solutions or outputting a PDF of your LaTeX file) by the date they are due. Solutions must be clearly written, using complete sentences when necessary, and composed in a concise manner. (Once you complete a solution, think about how you can explain in the clearest and most concise way possible). Solutions to problems will be emailed out after problems are graded. You are welcome to collaborate with classmates but must writeup solutions on your own and in your own words. The idea here is that you should be able to explain any solution you writeup without the aid of anything else. If I suspect that this is not the case I reserve the right to have you come into my office and present a solution on the blackboard. Furthermore, solutions copied directly from another student or from the internet will receive no points. Here is the BU CAS Code of Conduct.

Midterms

There will be two take home midterms. These will be similar to homework assignments but you will be given a few days to complete the problems, entirely on your own. The dates for these will be announced soon. You are not allowed to collaborate with each other on these problems, but can use notes from class and the textbook.

Grades

Your course grade will assigned as follows
  • Homework scores (60%)
  • Midterms (40%)

    • Learn From Anywhere and Classroom policies

  • Following BU's spring 2022 covid policy, please let me know as soon as possible if you have to miss class due to a covid related issue (either quarantine or taking care of a relative). I will then record the lectures you have to miss and provide them to you.
  • If I have to miss class for a covid-related issue I will contact the class by email as soon as possible to inform you of the plan for lectures (mostly like remotely given on zoom). Please check your BU email at least once a day.

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