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Module

MAS2802 : Differential Equations, Transforms and Waves (Inactive)

  • Inactive for Year: 2023/24
  • Module Leader(s): Professor Anvar Shukurov
  • 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 2 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System

Aims

To introduce a range of advanced concepts and methods for solving ordinary and partial differential equations.

Module summary

Many applications of mathematics lead to problems where the unknown is a function, a law expressing the dependence of a certain variable on others. Fundamental laws of nature often involve not only functions that characterise a certain phenomenon but also their rates of change in space and/or time. In such problems, the governing equation contains not only unknown functions but also their derivatives: these are differential equations.

This course continues the exploration of differential equation that started in Stage 1, with emphasis on methods to solve them, both exact and approximate. The essential elements in the theory of ordinary and partial differential equations, and their methods of solution, introduced in this course, provide the basis for specific studies in other modules. The methods that will be introduced, justified and practiced apply to a wide range of ordinary and partial differential equations. The course will focus on understanding and solving differential equations rather than on extensive physical interpretation (although this aspect certainly will be mentioned).

Outline Of Syllabus

•       A review of the fundamental concepts of ordinary and partial differential equations.
•       Series solutions.
•       Elements of the Sturm-Liouville theory.
•       Fourier series and Fourier transforms.
•       Wave equation: simple derivation in one spatial dimension, generalisation to three dimensions, fundamental properties (D’Alembert’s solution, phase speed, plane waves, superposition, standing and travelling waves), wave packets.
•       Second-order partial differential equations. Separation of variables in Cartesian coordinates: application to the wave, heat, Laplace’s and Poisson’s equations.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture51:005:00Drop ins
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study531:0053:00Preparation time for lectures, background reading, coursework review
Total100:00
Jointly Taught With
Code Title
PHY2031Differential Equations, Transforms and Waves
Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer:  a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
Exam Pairings
Module Code Module Title Semester Comment
Differential Equations, Transforms and Waves2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Assessment Rationale And Relationship

A substantial formal examination is appropriate for the assessment of the material in this module. The course assessments will will 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