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 EulerLagrange 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
