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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Variational Principles (MATH10087)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Differential Equations (MATH10066)
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Lagrangian Dynamics (PHYS10015) OR Hamiltonian Dynamics (PHYS11012)
Other requirements None
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Not being delivered
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
Reading List
Basic reading material consists of the course lecture notes.

Additional Information
Graduate Attributes and Skills Not entered
KeywordsVarP
Contacts
Course organiserProf Josť Figueroa-O'Farrill
Tel: (0131 6)50 5066
Email: j.m.figueroa@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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