Undergraduate Course: Variational Principles (MATH10087)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This is an introduction to variational principles in the context of classical mechanics. This course is intended as a second course on Dynamics, where the emphasis is to systematise classical dynamics by reformulating Newton's laws of motion as a variational principle. The Lagrangian and Hamiltonian formalisms introduced in this course serve as a conceptual basis for much of contemporary mathematical physics, as well as other branches of mathematics. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2014/15 Semester 1, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: None |
|
Web Timetable |
Web Timetable |
| Course Start Date |
15/09/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | MATH10087 Variational Principles | 2:00 | |
Summary of Intended Learning Outcomes
- Formulate variational principles
- Derive the Euler-Lagrange equations
- Use symmetries and conservation laws to solve the equations
- Ability to translate between Lagrangian and Hamiltonian formalisms
- Calculate effectively using Poisson brackets |
Assessment Information
| Coursework 5%, Examination 95% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
- (Review) Basic notions from several variable calculus.
- Fundamental lemma of the calculus of variations
- The Euler-Lagrange equations
- Second variation
- (Review) Newtonian mechanics
- (Review) Conservation laws
- Hamilton's principle of least action
- Noether's theorem and conservation laws
- Hamiltonian dynamics
- Conservation laws in Hamiltonian language
- Examples of variational problems
- Isoperimetric problems
- Lagrange multipliers
- Variational PDEs
- Noether's theorem revisited
- Elements of classical field theory |
| Transferable skills |
Not entered |
| Reading list |
Basic reading material consists of the course lecture notes.
|
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | VarP |
Contacts
| Course organiser | Prof José Figueroa-O'Farrill
Tel: (0131 6)50 5066
Email: j.m.figueroa@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
|
© Copyright 2014 The University of Edinburgh - 29 August 2014 4:20 am
|
University Homepage