Undergraduate Programme and Module Handbook 2026-2027
Module MATH3291: Partial Differential Equations III
Department: Mathematical Sciences
MATH3291: Partial Differential Equations III
| Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2026/2027 | Module Cap | Location | Durham |
|---|
Prerequisites
- Mathematical Methods II (MATH2811) OR Analysis in Many Variables II (MATH2031) AND Analysis I (MATH1051).
Corequisites
- None
Excluded Combination of Modules
- None
Aims
- To develop an understanding of the theory and methods of solution for Partial Differential Equations (PDEs).
Content
- First order equations and characteristics.
- Conservation laws and their weak solutions.
- Hyperbolic systems and their weak solutions
- Classification of general second order Partial Differential Equations
- Poisson, Laplace, Heat and Wave equations: existence and properties of solutions
Learning Outcomes
Subject-specific Knowledge:
- By the end of the module students will:
- Be able to solve seen and unseen problems on the given topics.
- Be able to reproduce theoretical mathematics in the field of Partial Differential Equations;
- Have a knowledge and understanding of fundamental theories and abstract concepts of this field demonstrated through one or more of the following topic areas: solution of first order equations and systems, and classification of second order PDEs and their solutions.
Subject-specific Skills:
- Students will have highly specialised and advanced mathematical skills which will be used with minimal guidance in the following areas: Analysis of PDEs.
- In addition, students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: abstract reasoning.
Key Skills:
- Students will develop mathematical skills in the following areas: abstract reasoning, problem solving.
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Problems classes show how to solve example problems in an ideal way, also revealing the thought processes behind such solutions.
- Formative assignments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
- Summative assignments test achievement of learning outcomes and provide feedback to students about their mastery of the topics.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.
Teaching Methods and Learning Hours
| Activity | Number | Frequency | Duration | Total/Hours | Attendance Monitored |
|---|---|---|---|---|---|
| Lectures | 40 | 2 per week for 20 weeks | 1 Hour | 40 | |
| Problem Classes | 10 | 4 in Michaelmas; 4 in Epiphany; 2 in Easter | 1 Hour | 10 | Yes ■ |
| Preparation and Reading | 150 | ||||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 70% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| On Campus Written Examination | 2 Hours | 100% | |
| Component: Summative Assignments | Component Weighting: 30% | ||
| Element | Length / duration | Element Weighting | Resit Opportunity |
| Assignment | 100% | ||
Formative Assessment:
Four assignments to be submitted.
■ Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.