Graduate courses are offered each year based on the interest of the students in the department. If you have any questions or comments, please contact Audrey via email (firstname.lastname@example.org).
Possible topics include but are not limited to: Why DDEs -- some examples of DDEs; concepts of functional differential equations; basic theory for DDEs; properties of solution semiflows of DDEs; stability theory (Liapunov functional and Razumikhim-type theorems); linear systems and characteristic equations; Hopf bifurcations in DDEs; monotone DDEs; numerical solutions of DDEs.
About the Course
Every engineer and scientist needs to know how to solve mathematical problems numerically. this course gives a coherent explanation of how to do so, and ahow to know when the answer is correct: if you do it right, the comuter will give you the exact answer to a nearby problem. Some problems are sensitive (aka "ill-conditioned") and this course teaches that, too. We use Matlab and a little Maple.
About the Textbook
Available for free in PDF formthrough UWO library, or in paperback via SpringerLink (through the library again) for $25USD, the book is "A Graduate Intorduction to NUmerical Analysis" by R. M. Corless and N. Fillion. This book was listed as the ACM "Best of 2013" when it was published. A review by Nick Higham (Manchester) can be found here. A review by Alex Townsend (Cornell) will appear in SIAM Review. The book was written here at Western, and many drafts were polished with the help of Engineering and Science Graduate students, since about 2010.
About the Instructor
R. M. Corless has been a Professor of Applied Mathematics at Western since 1987. His PhD was in Mechanical Engienering (UBC, wind engineering, under G. V. Parkinson). He has written three books, and over 170 articles of one sort or another and has been cited many thousands of times. He has won The Faculty of Science Teaching Award and in 2015-2016 his teaching ratings were 7/7 across the board.
This course introduces students to mathematical modelling for the life sciences primarily through the use of differential equations. Topics vary from year to year, but often include population biology, natural-resource management, epidemiology and disease dynamics, physiology, development and biochemistry. Students will learn (a) how to motivate, build and analyze differential-equation models, (b) how to interpret results in biological terms, and (c) how to communicate model predictions in plain language, and with reference to existing literature in the life sciences. In recent years, assessment has included tests, problem sets and a research project.
This seminar is a required course for the Scientific Computing collaborative program. It consists of seminars on interdisciplinary scientific computing methods given by students, researchers, and Compute-Canada/Sharcnet seminars.
Emphasis will be placed on understanding solutions and major phenomena for PDE. The course will be a balanced treatment about modeling and problem solving with PDE. Maple will be used to numerically and analytically solve problems. It will also be used to graph solutions to illustrate phenomena encountered during the course. This will be mostly through the use of programs that will be provided. No prior knowledge of Maple will be assumed. There will be some guest lectures in the course from the department, to emphasize the breadth and unity of the subject.