Undergraduate Course: Variational Principles (MATH10087)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | 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. |
| Course description |
- (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
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
|
| Academic year 2015/16, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| 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 )
|
| Assessment (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 5%, Examination 95% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | MATH10087 Variational Principles | 2:00 | |
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
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Reading List
Basic reading material consists of the course lecture notes.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | VarP |
Contacts
| Course organiser | Prof José Figueroa-O'Farrill
Tel: (0131 6)50 5066
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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