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Durham University

Postgraduate Module Handbook 2021/2022

Archive Module Description

This page is for the academic year 2021-22. The current handbook year is 2022-23

Department: Mathematical Sciences

MATH41720: Partial Differential Equations

Type Tied Level 4 Credits 20 Availability Available in 2021/22
Tied to G1K509 Mathematical Sciences

Prerequisites

  • Analysis in Many Variables.

Corequisites

  • None

Excluded Combination of Modules

  • None

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.
  • Reading material on one of the following topics: applications of PDEs, further theory of PDEs.

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.
  • have an advanced understanding in one of the following areas: applications of PDEs, further theory of PDEs
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.
  • Students will be able to study independently to further their knowledge of an advanced topic.

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.
  • Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
  • 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 written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.


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