Module manager: Adrian Barker
Email: A.J.Barker@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
MATH2350 Vector Calculus and Partial Differential Equations, AND MATH2400 Mathematical Modelling, AND MATH1013 Computational Mathematics and Modelling
| MATH1013 | Computational Mathematics and Modelling |
| MATH2350 | Vector Calculus and Partial Differential Equations |
| MATH2400 | Mathematical Modelling |
MATH3476 Numerical Methods
This module is not approved as a discovery module
The equations that model real-world problems can only rarely be solved exactly. The basic idea employed in this course is that of discretising the original continuous problem to obtain a discrete problem, or system of equations, that may be solved with the aid of a computer. This course introduces and applies the techniques of finite differences, numerical linear algebra and stochastic simulation
In this module, students will develop their understanding of the numerical methods used to solve problems involving ordinary and partial differential equations on a computer. This will involve practical python programming, as well as understanding the background theory for these numerical methods, including aspects of approximation theory and interpolation, numerical differentiation, linear algebraic techniques, as well as time-stepping methods. Students will apply these techniques in a number of examples that they implement in python.
On successful completion of the module students will be able to: 1. Work independently to acquire an understanding of the relevant background theory and to apply theory to solve problems involving ODEs and PDEs in practice. 2. Interpolate data on a 1-D interval and understand the Runge phenomenon. 3. Approximate partial derivatives by finite differences in both 1-and 2-D to pre-specified orders and accuracy. 4. Set up and solve linear systems of simultaneous algebraic equations for 1-D and 2-D elliptic Boundary Value Problems (e.g. obtained using finite difference methods). 5. Understand time-stepping methods so that they can solve PDE Initial Value Problems, relevant for the most important hyperbolic and parabolic PDEs arising in real-world problems. 6. Implement various numerical methods in python and understand how to interpret the results.
Introduction to the canonical types of PDEs and examples of where they arise in real-world problems in science, engineering and economics; · Introduction to approximation theory; · Numerical differentiation by finite differences in 1D and 2D; · Numerical linear algebra; · Solving ODE and 2D Elliptic PDE boundary value problems using finite differences and/or shooting; · Time-stepping methods for initial value problems involving ODEs and parabolic & hyperbolic PDEs; and · Stochastic simulation methods. Additional topics that build on these may be covered as time allows.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 44 | 1 | 44 |
| Private study hours | 156 | ||
| Total Contact hours | 44 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Several example sheets will be provided as the module progresses. Students will be encouraged to consider problems independently after reading the lecture notes and watching any pre-recorded videos, in collaboration with their peers, and/or making use of online resources. The lectures will discuss some of these examples, in addition to others contained within the lecture notes. Students will have opportunities for receiving formative feedback on their work and model solutions will be provided.
Check the module area in Minerva for your reading list
Last updated: 19/05/2026
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