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MATH3291: PARTIAL DIFFERENTIAL EQUATIONS III

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 3
Credits 20
Availability Available in 2023/24
Module Cap
Location Durham
Department Mathematical Sciences

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 Combinations 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

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week for 20 weeks and 2 in term 31 Hour42 
Problems Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 Hours100 

Formative Assessment

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

More information

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