Module manager: Dr Mike Evans
Email: r.m.l.evans@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2025/26
| MATH1000 | Core Mathematics |
Parts of MATH2365 & MATH2375
This module is not approved as a discovery module
Vector calculus is the extension of ordinary one-dimensional differential and integral calculus to higher dimensions, and provides the mathematical framework for the study of a wide variety of physical systems, such as fluid mechanics and electromagnetism. These systems give rise to partial differential equations (PDEs), which the students will learn to solve and analyse using techniques introduced in earlier modules as well as being introduced to Fourier methods for PDEs.
This module will introduce students to the mathematical tools for formulating and investigating coordinate-invariant laws of nature and their application to common physical systems involving scalar and vector fields.
On successful completion of the module students will have demonstrated the following learning outcomes:
1. Calculate vector and scalar derivatives of vector and scalar fields using the grad, div and curl operators in Cartesian and in cylindrical and spherical polar coordinates;
2. Change variables in two and three dimensional integrals using Jacobians;
3. Calculate line and surface integrals and use the various integral theorems;
4. Solve simple partial differential equations using separation of variables; and
5. Use Fourier series and Fourier transform techniques.
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a. Written communication
b. Manage workload and deadlines through prioritisation and productivity skills.
c. Maintain and uphold academic integrity and professional ethics.
d. Problem solving by formalising and analysing aspects of the natural world.
1. Grad, div, curl and the del operator. The directional derivative and Laplacian operators.
2. Conservative fields and their potentials. The divergence and Stokes theorems. Tangent and normal vectors.
3. Double and triple integrals. Transformation of coordinates: the Jacobian.
4. Line and surface integrals.
5. Fourier series and transforms.
6. Diffusion equation, wave equation, Laplace equation.
7. Rectangular, circular and spherical domains.
Additional topics that build on these may be covered as time allows. Further details of possible topics will be delivered closer to the time that the module runs.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 44 | 1 | 44 |
| Seminar | 10 | 1 | 10 |
| Private study hours | 146 | ||
| Total Contact hours | 54 | ||
| Total hours (100hr per 10 credits) | 200 | ||
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team