Joseph Webber | University of Warwick

Lecturing

In the 2025-26 academic year, I am the module lead and lecturer for MA4N4 Transport Processes in Mathematical Biology at the University of Warwick. Resources for this course can be found on the Moodle page, and I will post anything that can be shared more widely here.

Cambridge supervision resources

Over the course of my PhD I supervised courses in applied mathematics as part of the Cambridge Mathematical Tripos, as well as lectured portions of the Part IA Introduction to Mechanics course. I’ve collected some notes and resources here in case they’re of any use.

Part IB Methods and Variational Principles

Part IB Fluid Dynamics

Notes on the stress tensor - though not on the course at Part IB, this justifies the boundary conditions introduced here.
Notes on Kelvin’s circulation theorem - a derivation of Kelvin’s circulation theorem and its application to sheet 2 question 7.
Notes on water waves, specialising in the dynamic boundary condition; people often find this hard.
MATLAB code for a rough-and-ready visualisation of the flow field in the solution to 2019 Paper 1 Q17C.
Key to past exam questions (Excel spreadsheet) breaking down past exam questions from 2017-2021 by the sections of the schedules they are based on.

Part II Fluid Dynamics

Papkovich-Neuber potentials - again, not on the course, but useful solutions for Stokes flow.

Part III introductory videos

I have produced a playlist of videos on YouTube introducing the basics of fluid mechanics and continuum mechanics in general for students who studied their first undergraduate degree elsewhere. Click here to view all 10 videos on YouTube.