 Felix Kwok Département de mathématiques et de statistique Université Laval ## Current courses

### MAT 4410/7235 Résolution numérique des EDO et des EDP, Autumn 2022

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

### MAT 1900 Mathématiques de l'ingénieur 1, Autumn 2022

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.

## Past Courses

### Semester/full-year courses

• Analyse numérique matricielle, Université Laval, Winter 2022

• Mathématiques de l'ingénieur 1, Université Laval, Winter and Autumn 2021

• 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.

• Résolution numérique des EDO et des EDP, Université Laval, Autumn 2020 and 2021

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

• Calculus II, HKBU, Spring 2020

• Course Description: Integral Calculus: antiderivatives, definite integrals, techniques of integration. Applications: areas, volumes and surfaces. Parametric curves and polar coordinates. Introduction to infinite sequences and series, convergence tests, power series.

• Numerical Methods for Differential Equations, HKBU, Spring 2018 and 2020

• Course Description: The course serves as an introduction to numerical methods for ordinary and partial differential equations. The course will cover Runge-Kutta methods for initial value problems, shooting methods for two-point boundary value problems, finite difference, finite volume and finite element methods for elliptic problems, method of lines for diffusion problems, and upwind methods for hyperbolic problems. In addition to the theoretical properties of the numerical methods, emphasis will be placed on their implementation in MATLAB/Octave.

• Linear Algebra, HKBU, Autumn 2015, Autumn 2019

• Course Description: Introduction to linear equations, matrices, determinants, vector spaces and linear transformations, bases, inner products, orthogonality, eigenvalues and eigenvectors, diagonalization, least squares problems and other applications. The course emphasizes matrix and vector calculations and applications.

• Calculus I, HKBU Spring 2015, Spring and Autumn 2016, Autumn 2017, Spring and Autumn 2018

• Course Description: First course in differential and integral calculus. Topics include: Review of pre-calculus, limits and continuity, differentiation and its applications, indefinite and definite integrals, applications of integration.

• Estimating the World, HKBU, Autumn 2014

• Course Description: First-year numeracy course, with focus on the understanding and use of estimation in the context of complex, real-life applications. A few simple numerical techniques (root-finding, interpolation, least-squares fit and quadrature) are introduced to help with the modelling, and MATLAB is used to compute approximations of the relevant quantities. The aim is to improve students' ability to reason with quantitative information in daily life, so that they are able to ask pertinent questions and produce educated guesses through sensible assumptions and appropriate methodologies.

• Algèbre I, Université de Genève, Autumn 2013

• Course Description: First-year course on linear algebra. Contents include abstract vector spaces, linear maps, eigenvalues and eigenvectors, inner product spaces, spectral theorem.

• Analyse Numérique des Équations aux Dérivées Partielles, Université de Genève, Autumn 2012

• Course Description: Derivation of some PDEs of mathematical physics. Finite difference and finite volume methods. Spectral methods. Finite element methods: derivation and analysis. Time-dependent problems, CFL condition.

• Analyse Numérique, Université de Genève, 2010–11, 2011–12 and 2012–13 (full year)

• Course Description: Introduction to Scientific Computing and analysis of numerical algorithms. Topics include numerical integration, interpolation and approximation, numerical solution of ODEs, numerical linear algebra and least squares, eigenvalue problems, solution of nonlinear systems of equations.

• 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.

### Short courses

• 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

• Course Description: A six-hour mini-course (4 x 1.5 hours, fourth lecture given by H. Tchelepi) on iterative methods and multiphysics: examples of multiphysics problems, phase field and domain decomposition. Fixed point methods: Newton's method, stationary iterative methods for linear problems. Krylov methods and the conjugate gradient method: derivation and convergence, preconditioning.

• 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

• Course Description: A one-day introductory course on basic domain decomposition methods, consisting of three one-hour lectures on theoretical aspects in the morning and a three-hour practial session in the afternoon. The morning sessions consist of lectures on Schwarz methods, Dirichlet-Neumann and Neumann-Neumann methods, and on modern coarse spaces. During the aftenroon session, participants experiment with the above methods using sample Matlab codes.

• Dirichlet-Neumann and Neumann-Neumann methods, Summer School on Domain Decomposition Methods à Nice 2018, Université Côte d'Azur, France, June 19-21, 2018

• Course Description: A 1.5-hour lecture and a 2-hour practical session (with G. Ciaramella) during a three-day short course on domain decomposition methods. In the lecture portion, we introduce the Dirichlet-Neumann (DN) and Neumann-Neumann (NN) methods, which are naturally formulated on non-overlapping domain decompositions. We discuss their convergence behaviour on two subdomains, first in 1D, then in 2D using Fourier techniques seen in Lecture 1. The influence of geometry and relaxation parameters will be discussed, and we explain how these methods can be extended to yield FETI and BDDC methods, which are very powerful methods that can be used for problems with complicated geometries.

• Numerical Methods for Spectral Theory, 2016 CRM Summer School on Spectral Theory and Applications, Université Laval, Quebec, Canada, July 4–14, 2016

• Course Description: A 5-hour mini-course on numerical methods for spectral theory: finite difference and finite element methods for PDE eigenvalue problems, algorithms for matrix eigenvalue problems, applications to vibrating plates. Lecture notes and sample codes are available.

### Courses for which I was a TA

• 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