Patrick
Walls

Associate Professor
of Teaching

MATH 210

Introduction to Mathematical Computing

Learning Goals

  • Create computational narratives in Jupyter notebooks with explanatory text written in markdown, mathematical equations rendered with LaTeX and computations executed by Python code
  • Perform matrix computations with NumPy, create mathematical graphics with Matplotlib and implement mathematical algorithms with SciPy
  • Approximate solutions of non-linear equations
  • Approximate definite integrals and estimate error
  • Compute solutions of large linear systems of equation
  • Approximate solutions of ordinary differential equations

Resources

MATH 258

Differential Equations for Mechanical Engineering

Learning Goals

  • Compute analytical solutions of first and second order differential equations
  • Compute the Laplace transform of elementary functions and apply the tranform to differential equations
  • Describe qualitative properties of non-linear systems of differential equations by graphical methods
  • Create mathematical models of real-world phenomenon such as fluid mixing, friction, drag, vibrations and RLC circuits
  • Approximate and visualize solutions of differential equations with MATLAB

Resources

MATH 254

Multivariable and Vector Calculus for Mechanical Engineering

Learning Goals

  • Compute double and triple integrals in cartesian, polar and spherical coordinates
  • Compute partial derivatives of functions of several variables
  • Find extreme values of functions of several variables
  • Compute line and surface integrals of vector fields
  • Summarize integral equations given by the Divergence Theorem, Stokes Theorem and the Fundamental Theorem of Line Integrals
  • Create mathematical models of real-world phenomenon arising in fluid dynamics and thermodynamics
  • Approximate definite integrals and visualize curves and surfaces in 3D with MATLAB

Resources

MATH 307

Applied Linear Algebra

Learning Goals

  • Summarize properties and constructions of matrix decompositions LU, QR and SVD
  • Perform matrix computations using mathematical software Python, SciPy and Jupyter
  • Compute solutions of large systems of linear equations using matrix decompositions
  • Compute least squares approximations of large linear systems using matrix decompositions
  • Compute eigenvalues of large matrices using iterative methods
  • Analyze digital signals using the discrete Fourier transform
  • Create mathematical models of real-world phenomenon such as computed tomography and digital signal processing

Resources

MATH 441

Discrete Optimization Problems

Learning Goals

  • Formulate well-defined optimization problems based on real-world phenomena
  • Describe and contrast algorithms for solving optimization problems
  • Describe and contrast the computational complexity of optimization problems
  • Use mathematical software to compute solutions of optimization problems
  • Communicate solutions of optimization problems to a general mathematical audience

Resources

Mathematical Python

Mathematical Python is a web-based open textbook on mathematical computing with Python, SciPy and Jupyter. The book consists of 25+ Jupyter notebooks covering markdown and LaTeX, basic Python programming, NumPy, SciPy and matplotlib, optimization, numerical integration, linear systems equations, eigenvalues and eigenvectors, and ordinary differential equations.

Resources

mbgrader

mbgrader (math batch grader) is a custom web application for batch grading MATLAB assignments. The application is built with Python and Flask, SQLite and BackboneJS, and is used to grade assignments for MATH 152, MATH 221 and MATH 215/255 at UBC which total over 3000 students per year. In MATH 152 alone there are over 800 students and 6 MATLAB assignments and each assignment takes about 24 hours to assess when assignments are graded manually one at a time. With mbgrader, the same assignments can be graded in 2 hours. mbgrader also allows graders to provide thoughtful, individualized feedback to students since all responses are reduced to a small number of batches per question.

Resources

Course Map

A data visualization of the undergraduate mathematics program at UBC built with D3.

Resources

JupyterDays

Jupyter notebook is a web application for producing computational narratives: a notebook in the browser which runs code and renders text, mathematical notation, images and videos. Jupyter notebook is a powerful open source tool for scientific computing, reproducible research and teaching data science. JupyterDays is an opportunity for instructors, researchers and students at UBC to share their Jupyter experiences and to learn about new Jupyter tools.

Resources

UBCS3

UBC Scientific Software Seminar (UBCS3) aims to help students, fellows and faculty develop software skills for science.

Resources

Curriculum Vitae

Academic

Education

Awards

See CV (updated April 2024)

Contact

Department of Mathematics
The University of British Columbia
Room 229E, 1984 Mathematics Road
Vancouver, BC
Canada V6T 1Z2

pwalls@math.ubc.ca

patrickwalls

patrickjwalls

(604) 822-3045