Felix KwokDépartement de mathématiques et de statistique Université Laval |

*Course Description:*
Introductory course in mathematical modelling. Topics include: dimensional analysis, modelling
of chemical reactions using the law of mass action, Michealis-Menten kinetics; compartmental
models and epidemiological modelling; diffusion, random walks, heat equation and its solution by
Fourier transform; traffic flow, nonlinear conservation laws, method of characteristics and the
propagation of discontinuities; continuum mechanics, spatial and material coordinates, conservation
of mass and linear momentum. Reynolds transport theorem, stress-strain relations, Cauchy's stress
theorem.

*Course Description:*
Elements of matrix analysis: vector and matrix norms, eigenvalue and singular value decompositions,
conditioning of matrices and sensitivity to perturbations. Direct methods for solving linear systems:
Gaussian elimination, stability analysis, banded systems. Least squares problems and its conditioning,
solution by QR decomposition. Iterative methods: Jacobi, Gauss-Seidel and SOR iterations, convergence
analysis by spectral radius. Nonstationary methods: Richardson, conjugate gradients, GMRES and their
preconditioned versions.

*Course Description:*
Approximation of functions. Numerical integration. Numerical methods for systems of ordinary differential
equations. Finite difference methods for partial differential equations.

*Course Description:*
Complex numbers: definition and properties, rectangular and polar representations, locus of solutions to complex equations. Solution of ordinary differential equations: first order
equations, linear second order equations, order reduction. Differential
calculus of several variables, maxima and minima, constrained extrema.

- Analyse numérique matricielle, Université Laval, Winter 2022
- Mathématiques de l'ingénieur 1, Université Laval, Winter and Autumn 2021
- Résolution numérique des EDO et des EDP, Université Laval, Autumn 2020 and 2021
- Calculus II, HKBU, Spring 2020
- Numerical Methods for Differential Equations, HKBU, Spring 2018 and 2020
- Linear Algebra, HKBU, Autumn 2015, Autumn 2019
- Calculus I, HKBU Spring 2015, Spring and Autumn 2016, Autumn 2017, Spring and Autumn 2018
- Estimating the World, HKBU, Autumn 2014
- Algèbre I, Université de Genève, Autumn 2013
- Analyse Numérique des Équations aux Dérivées Partielles, Université de Genève, Autumn 2012
- Analyse Numérique, Université de Genève, 2010–11, 2011–12 and 2012–13 (full year)
- Mathématiques pour Informaticiens, Université de Genève, Winter 2010
*Course Description:*This is a first-year service course for computer science students. It covers topics in calculus and linear algebra usually seen in the second semester, such as differential and integral calculus in several variables, bilinear and quadratic forms, optimization and Fourier series. This course lays the theoretical foundations for the second-year numerical analysis course, which is mandatory for computer science students.

- Stationary Methods for Multiphysics Problems (with H. Tchelepi), 2021 CRM Summer School: Solving large systems efficiently in multiphysics numerical simulations, online, May 31-June 10, 2021
- Introductory Domain Decomposition Short Course (with L. Halpern and M.J. Gander), 25th International Conference on Domain Decomposition Methods, St. John's, Newfoundland and Laborador, Canada, July 22, 2018
- Dirichlet-Neumann and Neumann-Neumann methods, Summer School on Domain Decomposition Methods à Nice 2018, Université Côte d'Azur, France, June 19-21, 2018
- Numerical Methods for Spectral Theory, 2016 CRM Summer School on Spectral Theory and Applications, Université Laval, Quebec, Canada, July 4–14, 2016

- Analyse Numérique, Université de Genève, Autumn 2009
*Instructor: Dr. Sébastien Loisel* - Analyse Numérique, Université de Genève, 2008–09 (full year)
*Instructor: Prof. Martin Gander* - Analyse Numérique, Université de Genève, Winter 2008
*Instructor: Prof. Martin Gander* - Introduction to Scientific Computing, Stanford University, Winter 2004
*Instructor: Prof. Gene Golub* - Numerical Linear Algebra, Stanford University, Autumn 2003
*Instructor: Prof. Gene Golub* - Data Structures and Algorithms, McGill University, Autumn 2000 & 2001
*Instructor: Prof. Godfried Toussaint*

- A demo on Taylor series (Maple worksheet), prepared for Analyse I at Genève
- A demo on convergence of Steepest Descent and Conjugate Gradients (M-files), prepared for Analyse numérique at Genève
- A lecture on Chebyshev polynomials and splines, prepared for Introduction to Scientific Computing at Stanford
- A sample problem set with solutions, prepared for Introduction to Scientific Computing at Stanford