PHY3035 : Methods for Differential Equations
PHY3035 : Methods for Differential Equations
- Offered for Year: 2024/25
- Module Leader(s): Dr Toby Wood
- 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 1 Credit Value: | 10 |
ECTS Credits: | 5.0 |
European Credit Transfer System | |
Pre-requisite
Modules you must have done previously to study this module
Code | Title |
---|---|
PHY2026 | Vector Calculus |
PHY2031 | Differential Equations, Transforms and Waves |
Pre Requisite Comment
N/A
Co-Requisite
Modules you need to take at the same time
Co Requisite Comment
N/A
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 problems: uniqueness and existence of solutions.
• Separation of variables for 2nd order PDEs in cylindrical and spherical coordinates: Laplace equation and spherical harmonics.
• The Fourier transform and its applications to PDEs.
• Green's functions for PDEs: application to Laplace and Poisson equations.
Learning Outcomes
Intended Knowledge Outcomes
Students will learn the theory and applications of differential equations, and become able to identify
and apply appropriate methods for solving the equations, and interpret the solutions.
Intended Skill Outcomes
Students will be able to recognise standard types of ordinary and partial differential equations and be able to solve them using a variety of methods.
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 | 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 assessment |
Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Lecture preparation, background reading, coursework review |
Total | 100:00 |
Jointly Taught With
Code | Title |
---|---|
MAS3801 | Methods for Differential Equations |
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-level 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.
Reading Lists
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 | 1 | A | 80 | N/A |
Exam Pairings
Module Code | Module Title | Semester | Comment |
---|---|---|---|
Methods for Differential Equations | 1 | N/A |
Other Assessment
Description | Semester | When Set | Percentage | Comment |
---|---|---|---|---|
Prob solv exercises | 1 | M | 5 | Problem-solving exercise assessment |
Prob solv exercises | 1 | M | 5 | Problem-solving exercise assessment |
Prob solv exercises | 1 | M | 5 | Problem-solving exercise assessment |
Prob solv exercises | 1 | M | 5 | Problem-solving exercise 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.
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- PHY3035's Timetable
Past Exam Papers
- Exam Papers Online : www.ncl.ac.uk/exam.papers/
- PHY3035's past Exam Papers
General Notes
N/A
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The information contained within the Module Catalogue relates to the 2024 academic year.
In accordance with University Terms and Conditions, the University makes all reasonable efforts to deliver the modules as described.
Modules may be amended on an annual basis to take account of changing staff expertise, developments in the discipline, the requirements of external bodies and partners, and student feedback. Module information for the 2025/26 entry will be published here in early-April 2025. Queries about information in the Module Catalogue should in the first instance be addressed to your School Office.