Undergraduate Course: Variational Calculus (MATH11179)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Year 5 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  NB. This course is delivered *biennially* with the next instance being in 202223. 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: EulerLagrange 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

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of any prerequisite course listed above before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2022/23, 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
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20% Exam 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Variational Calculus (MATH11179)  2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Derive the EulerLagrange equations for variational problems, including the case of general variations.
 Derive conserved quantities from symmetries, and use them to solve the EulerLagrange equations.
 Solve variational problems with constraints: both algebraic and isoperimetric.
 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 
Keywords  VarC 
Contacts
Course organiser  Dr Jelle Hartong
Tel:
Email: jhartong@exseed.ed.ac.uk 
Course secretary  Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk 

