Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2025/26
| MATH1000 | Core Mathematics |
This module is not approved as a discovery module
This module introduces analytical and computational techniques for the solution of ordinary and partial differential equations, which describe particle motion in fields, fluids, waves, diffusion and many other phenomena.
This module will introduce students to the mathematical tools for formulating and investigating differential equations in a variety of physical settings. Some basic physical phenomena will also be presented, and students will see how underlying physical principles get expressed as differential equations.
On successful completion of the module students will have demonstrated the following learning outcomes:
1. Model physical phenomena with the Poisson equation
2. Model fluid flows using Laplace's equation
3. Study the solutions of ordinary differential equations using analytical and numerical techniques
4. Determine the stability of an equilibrium point and identify bifurcations
5. Write down suitable numerical schemes for solving ordinary differential equations.
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a. Communication
b. Technical/IT skills
c. Problem solving and analytical skills
d. Critical Thinking
e. Creativity
f. Systems thinking
g. Self-confidence, initiative and perseverance
h. Academic writing
1. Vector calculus: suffix notation, gravitation, electrostatics.
2. Mathematical modelling of fluids: elementary kinematics.
3. Vorticity and potential flows. Methods of solution of Laplace equation.
4. Existence and uniqueness of ordinary differential equations.
5. First order nonlinear ODEs: stability of equilibria, phase portraits, and bifurcations.
6. Numerical solution of ODEs: convergence, stability, and practical implementation.
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