• Math 400 material from the course I taught in the Spring of 2021 during COVID lockdown:
  • Online lecture playlist on YouTube with a file of the Lecture Notes.
  • Prepared Lecture Notes.
  • Assignments and midterms, with solutions to part A problems.

• I gave a series of lectures to a mixed senior undergraduate and graduate student audience at the South University of Science and Technology in Shenzhen, China, in June/July, 2018. I called the series, "A survey of applied mathematics techniques."
  • Syllabus.
  • Lecture #1 Function Spaces, Finite Difference Methods & Green's Functions. Accompanying MATLAB code: dGvalidate.m that motivates the form and validates the expression found for the inverse matrix of the finite difference discretization.
  • Lecture #2 Finite Difference Methods. Accompanying MATLAB code: probA.m that computes a test problem with an FD approximation.
  • Lecture #3 Modelling, Scaling, and Nonlinear Problems Accompanying MATLAB code: probA_nonlinear.m that compu tes the nonlinear example problem in the notes with an FD approximation.
  • Lecture #4 Series Solutions, Sturm-Liouville Problems, Spectral Methods. Accompanying MATLAB code: pcg.zip Preconditioned Conjugate Gradient Solve of a non-constant coefficient boundary value problem.
  • Lecture #5 Interpolation, Quadrature, and Collocation Methods. Accompanying MATLAB code of bvp4c examples: bvp_probA.m, bvp_probA_nonlin.m, bvp_eigen.m.
  • Lecture #6 Asymptotic Methods. Typewritten with an additional section on the Allen Cahn equations.
  • Lecture #7 The Finite Element Method.
  • Lecture #8 Time Stepping Methods.

• The Solution of Partial Differential Equations by Marvin Shinbrot. These are the lecture notes that I first learned this material from.

• IAM Data Science Pre-Workshop Lectures:
  • Linear Algebra Lecture #1 (linear systems, condition number, sparse matrices, and the Conjugate Gradient method) and companion Jupyter notebook.
  • Linear Algebra Lecture #2 (optimization, least squares, vector Newton's method) and companion Jupyter notebook.
  • Linear Algebra Lecture #3 (Eigenanalysis, fast transform methods, singular value decomposition, principle component analysis) and companion Jupyter notebook.

• Math 152: Linear Systems. I used to maintain these typeset online notes for the course. They cover the complete course with many worked examples and many problems with solutions. MATLAB material is intergrated.

• Math 400: Applied Partial Differential Equations. These are from the course I taught in 2012, although I had taught it a few times previously. The file contains handwritten notes, assignments, midterm and final with solutions.

• Math 401: Green's Funcations and Variational Methods. These are from the course I taught in 2007. This was probably the most fun class I have ever taught, with 25 of the top students in Science that year. The file contains handwritten notes, assignments, midterm and final with solutions.

• Math 405: Numerical Methods for Differential Equations. These are from the course I taught in 2014. The file contains handwritten notes, assignments, midterm and final with solutions. There are preliminary notes on the Fourier Transform and Scaling and Nondimensionalization.

• Math 521: Finite Element Method. These are from the course I taught in 2014. The file contains handwritten notes and assignments. There are preliminary notes on Finite Difference Methods and Scaling and Nondimensionalization.

• Grade 5 workshop problems: In the Spring of 2005 I gave a series of workshops to a small group of grade 5 students at Queen Victoria Annex School in Vancouver. These are targeted at motivated, bright but not necessarily "gifted" students. The first few also have problem solutions.

• Courant Institute Written Comprehensive Exams, previous to 1987 (I deleted the pages that were blank, they are not missing). I took the exams in September, 1988. I see UBC graduate math students stressing over their exams and it made me remember my own experience. The pain has diminished substantially with the passing of time.

• Notes I made for my Oral Qualifying exams which I took in 1989, Parts I and II. I knew some things then that I don't remember now.

If I were ever to write a textbook, it would be on applied and computational PDE with the material from 400, 401 and 405.