Aims

To present basic ideas and techniques of variational calculus, and Lagrangian dynamics.

Outline Of Syllabus

Review of standard methods for finding extrema. Definition of, and method for calculating, extremals (minima/maxima) of functionals. The Euler-Lagrange equation. Classical examples from different disciplines. Lagrange multipliers. Multiple fields and variables.

The action principle and the Lagrangian, Generalized momenta. Euler angles. Hamiltonian dynamics, with applications to astro- and particle physics.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.