Undergraduate Programme and Module Handbook 2024-2025

# Module MATH3291: PARTIAL DIFFERENTIAL EQUATIONS III

## Department: Mathematical Sciences

### MATH3291: PARTIAL DIFFERENTIAL EQUATIONS III

Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

- Analysis in Many Variables II (MATH2031) and 20 additional credits of Level 2 mathematics modules; alternatively Analysis in Many Variables II (MATH2031) and Analysis I (MATH1051) (if taken in Year 2).

#### Corequisites

- One 20 credit Level 3 mathematics module.

#### Excluded Combination of Modules

#### Aims

- To develop an understanding of the theory and methods of solution for Partial Differential Equations.

#### Content

- First order equations and characteristics.Conservation laws and their weak solutions.
- Systems of first-order equations and Riemann invariants.
- Hyperbolic systems and their weak solutions
- Classification of general second order PDEs
- 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 problems in Partial Differential Equations;
- have an understanding of theoretical mathematics in the field of Partial Differential Equations;
- have mastered a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
- Solution of first order equations and systems.
- Classification of second order PDEs, and their solutions.

Subject-specific Skills:

- Students will have highly specialised and advanced mathematical skills in the following areas: Modelling and Analysis of PDEs

Key Skills:

- Students will have an appreciation of important Partial Differential Equations and their fundamental properties.

#### 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.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- 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 | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week for 20 weeks and 2 in term 3 | 1 Hour | 42 | |

Problems Classes | 8 | Four in each of terms 1 and 2 | 1 Hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 Hours | 100% |

#### Formative Assessment:

Eight assignments to be submitted.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University