- Offered for Year: 2023/24
- Module Leader(s): Professor Ian Moss
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
|
Semester 2 Credit Value:
|
10
|
|
ECTS Credits:
|
5.0
|
Aims
To present basic ideas and techniques of variational calculus, including relevant applications.
Module Summary
What is the shortest route between two places on the Earth's surface (the answer isn't a straight line, because the Earth isn't flat!)? How to run a utilitarian economy? How do you reformulate dynamical motion in terms of geometry? To answer questions such as these, we need a way to find the path between two points which minimises some quantity (such as length or time). The calculus of variations is a very elegant and powerful way of doing this, and consequently has wide application to real-world problems. The ideas provide the basis for a reformulation of dynamics which underpins modern theoretical physics.
Outline Of Syllabus
Review of standard methods for finding extrema. Definition of, and method for calculating, extremals
(minima/maxima) of functionals. The Euler-Lagrange equation. Classical examples from different disciplines.
Lagrange multipliers. Many dependent variables. The action principle, Lagrangian
and Hamiltonian dynamics with applications to astro- and particle physics.
Teaching Methods
Teaching Activities
| Category |
Activity |
Number |
Length |
Student Hours |
Comment |
|---|
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
| 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 | 20 | 1:00 | 20:00 | Formal Lectures |
| Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Total | | | | 100:00 | |
Jointly Taught With
| Code |
Title |
|---|
| MAS3809 | Variational Methods and Lagrangian Dynamics |
| MAS8809 | Variational Methods and Lagrangian Dynamics |
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 |
|---|
| MAS3809 | Variational Methods and Lagrangian Dynamics | 2 | N/A |
| MAS8809 | Variational Methods and Lagrangian Dynamics | 2 | N/A |
Other Assessment
| Description |
Semester |
When Set |
Percentage |
Comment |
|---|
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 2 | 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 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
