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Module

MAS3801 : Methods for Differential Equations

  • Offered for Year: 2023/24
  • Module Leader(s): Dr Toby Wood
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System

Aims

Introduce a range of advanced methods for solving ordinary and partial differential equations.

Module Summary
Most mathematical models are formulated in terms of differential equations. This module will introduce a range of topics from the theory of differential equations that have proved to be useful in solving practical problems. Equal emphasis will be placed on the theorems that underly the methods, the technical skills required to apply them and the meaning of the results. Illustrative problems will be drawn from a wide range of practical applications.

Outline Of Syllabus

•       Eigenfunction methods: Hermitian operators, Sturm-Liouville equations.

•       Special functions: Legendre functions, Bessel functions.

•       Well-posed problems: uniqueness and existence of solutions.

•       Separation of variables for 2nd order PDEs in cylindrical and spherical coordinates: Laplace equation and spherical harmonics.

•       The Fourier transform and its applications to PDEs.

•       Green's functions for PDEs: application to Laplace and Poisson equations.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Guided Independent StudyIndependent study581:0058:00Lecture preparation, background reading, coursework review
Total100:00
Jointly Taught With
Code Title
PHY3035Methods for Differential Equations
Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-level thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A80N/A
Exam Pairings
Module Code Module Title Semester Comment
1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable