PHY2031 : Differential Equations, Transforms and Waves
- Offered for Year: 2024/25
- Available for Study Abroad and Exchange students, subject to proof of pre-requisite knowledge.
- 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 Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision lectures |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal lectures |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Drop ins |
| Guided Independent Study | Independent study | 53 | 1:00 | 53:00 | Preparation time for lectures, background reading, coursework review |
| Total | 100:00 |
Jointly Taught With
| Code | Title |
|---|---|
| MAS2802 | Differential 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 Examination | 120 | 2 | A | 80 | N/A |
Exam Pairings
| Module Code | Module Title | Semester | Comment |
|---|---|---|---|
| Differential Equations, Transforms and Waves | 2 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 6 | Problem-solving exercises assessment |
| Prob solv exercises | 2 | M | 7 | Problem-solving exercises assessment |
| Prob solv exercises | 2 | M | 7 | Problem-solving exercises assessment |
Formative Assessments
Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.
| Description | Semester | When Set | Comment |
|---|---|---|---|
| Prob solv exercises | 2 | M | Problem Solving Exercises Formative 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
- Timetable Website: www.ncl.ac.uk/timetable/
- PHY2031's Timetable