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Module

MAS2802 : Differential Equations, Transforms and Waves

  • Offered for Year: 2024/25
  • 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 the mathematics needed to formulate and solve problems involving ordinary and partial differential equations.

Module Summary

This module continues the exploration of differential equations 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 module, provide the basis for specific studies in other modules. Fourier series and transform will be introduced in this context. The methods that will be introduced, justified and practiced apply to a wide range of ordinary and partial differential equations.

Outline Of Syllabus

A review of ordinary and partial differential equations;

Series solutions of ordinary differential equations.

Fourier series and Fourier transform.

Second-order partial differential equations. Separation of variables in Cartesian coordinates: application to the wave, heat and Laplace’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

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order 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 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 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.

Exam 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