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 (akager@uwo.ca).

This course assumes no previous experience in symbolic computation. The computer algebra system used in the course will be Maple, which is free to all Western students. The course has two aims: (1) to give students a toolbox of symbolic methods which they may apply in their own area of research, and (2) an understanding of some of the important algorithms used within computer algebra systems. Instruction format includes laboratory sessions using Maple, together with lectures on algorithms. Assessment will be largely based on Maple projects, which will be decided in consultation with the student.

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.

- The principles of theoretical evolutionary genetics will be covered, including models of selection, mutation and genetic drift. Stochastic modelling, including Wright-Fisher approaches and the Kolmogorov backward and forward (Fokker–Planck) equations will be emphasized. /li>

Topics covered include stability and bifurcation, Hopf bifurcation, limit cycles, Bogdanov- Takens bifurcation and homoclinic/heteroclinic bifurcations, center manifold theory and normal form theory, perturbation methods and Melinikov’s method.

- Random Number Generators
- Monte Carlo Integration: Hit/Miss Integration
- Random Walks (RW)
- Solving Laplace's Equation (and other DE's) using RW
- Percolation and modelling of Forest Fires
- Cellular Automata: Lattice Gas, Kauffman Model
- Monte Carlo Simulation: Ising Model
- Damage spreading, Fractals, Chaos
- Molecular Dynamics: Hard Spheres and more
- Other interesting things I like

- Introduction and Disclaimers
- Finite elements introduced as bars forming a truss
- Some mathematical aspects
- Towards a systematic method
- The matrix approach
- Two-dimensional heat flow
- Variational form
- The Galerkin approach
- Element computation
- Other topics not in the main text book

The goal of this course is both to introduce students to high performance computing methods, and in particular parallel programming paradigms. Students will work on projects using MPI and CUDA, OpenCL, and some basic Monte Carlo and stocastic methods.