Undergraduate

modules

Modules

MAS3801 : Methods for Differential Equations

Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

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 PDE problems: uniqueness and existence of solutions.
•       Separation of variables for 2nd order PDEs in cylindrical and spherical coordinates: Laplace equation and spherical harmonics, spherical waves.
•       The Fourier transform and it 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 ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Guided Independent StudyIndependent study127:0027:00Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and course test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Total100:00
Jointly Taught With
Code Title
PHY3035Methods of Differential Equations
Teaching Rationale And Relationship

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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A90N/A
Exam Pairings
Module Code Module Title Semester Comment
PHY3035Methods of Differential Equations1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Coursework assignments
Prob solv exercises1M5Course test
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The written exercises are expected to consist of two assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and the (in class) coursework test 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 are thus formative as well as summative assessments.

Reading Lists

Timetable