Getting Started
Working with the material
Everything here is written in Python. Marimo runs in your browser for lectures and exploring. Jupyter is what you'll use to save work and submit assignments.
Guides
Python Basics — new to programming?
Chapter 0
Welcome week: can a computer get a simulation wrong?
A small-group taste of the programming side of MATH4120: predict what a numerical method will do, then watch it happen.
Welcome Week Activity — Friday 2 October 2026
Chapter 1
What is a mathematical model?
The modelling cycle; units and dimensions; first ODEs from rate laws; difference equations.
Week 1 · 5–9 Oct
Lectures Mon 5 Oct 11:00 · Tue 6 Oct 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 9 Oct 11:00–13:00
Cavendish LT · lecture, then lab
Chapter 2
Dimensional analysis and nondimensionalisation
Characteristic scales; nondimensionalising an ODE; solution collapse.
Week 2 · 12–16 Oct
Lectures Mon 12 Oct 11:00 · Tue 13 Oct 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 16 Oct 11:00–13:00
Cavendish LT · lecture, then lab
Due: Handwritten exercise 1 — Fri 16 Oct, 16:00 Details ↓
Chapter 3
The Buckingham Π-theorem and the dimension matrix
Dimension matrices; finding Π-groups systematically; similarity and scaling laws.
Week 3 · 19–23 Oct
Lectures Mon 19 Oct 11:00 · Tue 20 Oct 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 23 Oct 11:00–13:00
Cavendish LT · lecture, then lab
Due: Computational assignment 1 — Fri 23 Oct, 16:00 Details ↓
Chapter 4
Ordinary differential equations
Separable equations; integrating factor; Bernoulli; second-order constant-coefficient ODEs; simple harmonic motion; damped oscillations.
Week 4 · 26–30 Oct
Lectures Mon 26 Oct 11:00 · Tue 27 Oct 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 30 Oct 11:00–13:00
Cavendish LT · lecture, then lab
Due: Handwritten exercise 2 — Fri 30 Oct, 16:00 Details ↓
Week 5 · 2–6 Nov
Lectures Mon 2 Nov 11:00 · Tue 3 Nov 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 6 Nov 11:00–13:00
Cavendish LT · lecture, then lab
Due: Handwritten exercise 3 — Fri 6 Nov, 16:00 Details ↓
Chapter 5
Single species models
Exponential and logistic growth; equilibria and stability; harvesting; bifurcation diagrams.
Week 6 · 9–13 Nov
Lectures Mon 9 Nov 11:00 · Tue 10 Nov 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 13 Nov 11:00–13:00
Cavendish LT · lecture, then lab
Due: Computational assignment 2 — Fri 13 Nov, 16:00 Details ↓
Chapter 6
Numerical solution of ODEs
Euler’s method; Heun’s method; error analysis; systems of ODEs; Lotka–Volterra and Van der Pol worked examples.
Week 7 · 16–20 Nov
Lectures Mon 16 Nov 11:00 · Tue 17 Nov 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 20 Nov 11:00–13:00
Cavendish LT · lecture, then lab
Due: Mid-semester test — Thu 19 Nov, 09:00–11:00 Details ↓
Week 8 · 23–27 Nov
Lectures Mon 23 Nov 11:00 · Tue 24 Nov 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 27 Nov 11:00–13:00
Cavendish LT · lecture, then lab
Chapter 7
Data-driven modelling with neural networks
When equations aren’t available; function approximation; feedforward networks; training; mechanistic vs data-driven models.
Week 9 · 30 Nov – 4 Dec
Lectures Mon 30 Nov 11:00 · Tue 1 Dec 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 4 Dec 11:00–13:00
Cavendish LT · lecture, then lab
Due: Handwritten exercise 4 — Fri 4 Dec, 16:00 Details ↓
Week 10 · 7–11 Dec
Lectures Mon 7 Dec 11:00 · Tue 8 Dec 13:00
Faraday LT (Mon), Frankland LT (Tue)
Workshop
Your group’s time and room are on your timetable
Details to follow
Computing lecture Fri 11 Dec 11:00–13:00
Cavendish LT · lecture, then lab
Due: Group project — Fri 11 Dec, 16:00 Details ↓
Assessment
Coursework, test and exam
Coursework is 30% of the module: four handwritten exercises and two computational assignments (3⅓% each), plus a group project (10%). The mid-semester test is 20% and the exam 50%. Everything is submitted on Moodle.
Handwritten exercise 1 · Chapter 1
Out Fri 9 Oct · due Fri 16 Oct, 16:00
Handwritten; scanned PDF via Moodle · marked out of 20
Computational assignment 1 · Numerical integration
Out Mon 12 Oct · due Fri 23 Oct, 16:00
Moodle quiz, automatically graded (CodeRunner)
Handwritten exercise 2 · Chapters 2–3
Out Mon 19 Oct · due Fri 30 Oct, 16:00
Handwritten; scanned PDF via Moodle · marked out of 20
Handwritten exercise 3 · Chapter 4
Out Mon 26 Oct · due Fri 6 Nov, 16:00
Handwritten; scanned PDF via Moodle · marked out of 20
Computational assignment 2 · Numerical differentiation
Out Mon 2 Nov · due Fri 13 Nov, 16:00
Jupyter notebook (.ipynb) submitted on Moodle
Mid-semester test · 20% of the module
Thu 19 Nov, 09:00–11:00
In person, invigilated · your room is on your timetable
Handwritten exercise 4 · Chapter 5
Out Fri 20 Nov · due Fri 4 Dec, 16:00
Handwritten; scanned PDF via Moodle · marked out of 20
Group project · 10% of the module
Out Mon 23 Nov · due Fri 11 Dec, 16:00
Group submission on Moodle