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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Variational Calculus (MATH11179)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryNB. This course is delivered *biennially* with the next instance being in 2016-17. It is anticipated that it would then be delivered every other session thereafter.

This is a course on the calculus of variations and explores a number of variational principles, such as Hamilton's Principle of Least Action and Shannon's Principle of Maximum Entropy. The approach taken in this course lies at the interface of two disciplines: Geometry and Mathematical Physics. In Geometry you will learn about geodesics, minimal surfaces, etc. In Physics you will learn to elevate Newton's laws to a mathematical principle and discuss lagrangian and hamiltonian formulations. A running theme will be the relationship between symmetries and conservation laws, as illustrated by a celebrated theorem of Emmy Noether's. We will not assume, however, any background in either Physics or Geometry. All the necessary vocabulary and concepts will be introduced in the course.
Course description - Calculus of variations: Euler-Lagrange equations, general variations
- Newtonian mechanics and conservation laws
- Hamilton's principle of least action
- Noether's theorem
- Hamiltonian formalism
- Isoperimetric problems
- Holonomic and nonholonomic constraints
- Variational PDEs
- Noether's theorem revisited
- Classical field theory
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Differential Equations (MATH10066)
Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of any pre-requisite course listed above before enrolling.
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. derive the Euler-Lagrange equations for variational problems, including the case of general variations
  2. derive conserved quantities from symmetries, and use them to solve the Euler-Lagrange equations
  3. solve variational problems with constraints: both algebraic and isoperimetric
  4. calculate effectively using Poisson brackets
Reading List
Lecture notes will be provided, which contain ample bibliography with other sources.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsVarC
Contacts
Course organiserProf Josť Figueroa-O'Farrill
Tel: (0131 6)50 5066
Email: j.m.figueroa@ed.ac.uk
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk
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