MSP2802
Differential Equations, Transforms and Waves
- Offered for Year: 2025/26
- Module Leader(s): Dr Matthew Crowe
- Owning School: School of 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 |
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.
Learning Outcomes
Intended Knowledge Outcomes
Students will know:
- The power-series representations for the solutions of ordinary differential equations.
- The notion of the orthogonality of functions.
- The meaning and applications of Fourier series and transform.
- Laplace’s, heat and wave equations, methods of their solution in Cartesian coordinates.
Intended Skill Outcomes
Students will be able to:
- Construct power series solutions of ordinary differential equations.
- Represent a wide class of functions as Fourier series.
- Find separable solutions for suitable partial differential equations.
- Perform direct and inverse Fourier transforms of simple functions.
Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Drop-In's |
| Guided Independent Study | Independent study | 53 | 1:00 | 53:00 | Preparation time for lectures, background reading, coursework review |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in-course assessments |
| Totals | 100 |
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
| Component | Length (mins) | Semester | When set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination 1 | 120 | 1 | A | 85 | N/A |
Other Assessments
| Component | Semester | When set | Percentage | Comment |
|---|---|---|---|---|
| Problem solving exercises 1 | 1 | M | 5 | Problem-solving exercises assessment |
| Problem solving exercises 2 | 1 | M | 5 | Problem-solving exercises assessment |
| Problem solving exercises 3 | 1 | M | 5 | Problem-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 that one way 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.
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/