Math-597: Topics in Applied Mathematics: Delay Differential Equations, Fall 2018

Course Outline

• Coordinates:
  Lectures: Tues 4.30-6pm in BH-1214 and Thursdays 4.00-5.30pm in BH-1205.
  First class on Tuesday 11th September, and last class on Thursday 29th November.
  Prof Humphries, BH-1112, Tel: 398-3821, E-mail: humphries@math.mcgill.ca
  Office Hours: Thursdays after class, and by arrangement - this is the only class I teach this semester so I can be quite flexible on meeting times, just send me an email.
  

• Introduction
  Many physical processes are modelled by differential equations which involve delays. This course will provide an introduction to delay differential equations (DDEs) suitable for graduate students or upper level honours students with the correct background.

  This course will concentrate on the key tools needed to understand the behaviour of these equations, and also some of numerical techniques used to approximate solutions. Throughout we will emphasise the similarities and differences between DDEs and ordinary differential equations.

  Topics covered will include: DDEs as infinite dimensional dynamical systems, breaking points and smoothing of DDE solutions, continuous Runge-Kutta methods for ODEs and DDEs, linear stability of steady states, bifurcation theory. A selection of more advanced topics will also be covered. The choice of topics will depend on time and the preferences of the participants, but may include state-dependent delays, distributed delays, numerical continuation and bifurcation techniques.

• References:
  There in no required text book for this course. However some material from the following texts may be useful:
  • An Introduction to Delay Differential Equations with Applications to the Life Sciences, Hal Smith, Springer 2010. This book is available free online at McGill, see http://www.springerlink.com/content/978-1-4419-7645-1/. Note that if you do want to buy a paperback copy, its only $24.95 if you buy it by clicking the link on that page. From off campus try this link.
  • Numerical Methods for Delay Differential Equations, Alfredo Bellen and Marino Zennaro, OUP 2003. This book is also available free online from McGill (which is good because the print version is ridiculously expensive). See DOI:10.1093/acprof:oso/9780198506546.001.0001 or McGill WorldCat link.

• Prerequisites:
  The course is suitable for graduate students or upper level honours undergraduate students in mathematics. There are no explicit prerequisites other than having a suitable level of mathematical maturity. In particular, it is not required to have previous knowledge of delay differential equations -- these are not included in standard curricula so I will not assume any previous knowledge.

  It would be very useful, but not essential, to have some knowledge of dynamical systems and numerical analysis.

• Registration:
  Be aware that there are two Math597 courses in the Fall semester. This course is Section 2 (while Section 1 is Convex Optimization).

  PhD students should register in Math761 Section 2, while Masters students and undergraduates should register in Math597 Section 2. Contact me to obtain the form that you need in order to register.

  The course is open to undergraduate honours applied mathematics or honours mathematics students. To register in math597 you should have completed at least 30 credits in required or complementary courses from the Honours in Applied Mathematics program, and have the permission of the Department of Mathematics and Statistics. If you are interested in following the course but do not satisfy those conditions please contact me.

• Assessment:
  There will not be regular assignments or a midterm or final exam. Students will complete a project, and will be graded on their oral presentation of this project to the class. Project topics must be approved by the instructor, and may be based on sections of a book or research papers. The project will count 90% of the final grade, with the other 10% awarded for participation.

• Copyright
  Instructor generated course materials (e.g., handouts, notes, summaries, exam questions, etc.) are protected by law and may not be copied or distributed in any form or in any medium without explicit permission of the instructor. Note that infringements of copyright can be subject to follow up by the University under the Code of Student Conduct and Disciplinary Procedures.

• Academic Integrity
  The work you hand in should be your own effort; any collaboration must be acknowledged.

  McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/students/srr/honest/ for more information).

• Language
  In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.