# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2014/2015 Archive for reference only THIS PAGE IS OUT OF DATE

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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

# Undergraduate Course: Symmetries of Classical Mechanics (PHYS10088)

 School School of Physics and Astronomy College College of Science and Engineering Credit level (Normal year taken) SCQF Level 10 (Year 3 Undergraduate) Availability Available to all students SCQF Credits 10 ECTS Credits 5 Summary This course provides an introduction to rotational space and space-time symmetries in classical physics. Topics covered include: vectors, bases, matrices determinants and the index notation; the general theory of Cartesian tensors; rotation and reflection symmetries; various applications including elasticity theory - stress and strain tensors. The latter part of the course applies covariant and contravariant tensor analysis to special relativity. After an introduction to the physical basis of special relativity and Lorentz symmetry transformations there follows the covariant formulation of classical mechanics and electromagnetism including: force, momentum and velocity 4 vectors, the Maxwell tensor and particle collisions. Course description - Vectors, matrices, determinants, the delta and epsilon symbols - Rotational symmetry: transformation of bases, reflections, passive and active transformations - Definition and transformation properties under rotations of Cartesian tensors, quotient theorem, pseudotensors, isotropic tensors - Taylor's theorem: the one- and three-dimensional cases - Some examples of tensors: *conductivity tensor *moment of inertia tensor and diagonalisation of rank-2 tensors *continuum mechanics, the strain and stress tensors, Hooke's Law for isotropic media, fluid mechanics, the Navier--Stokes equation - Non-orthogonal co-ordinates, covariant and contravariant tensors - Physical basis of Special Relativity, inertial systems, constancy of the speed of light, Einstein's postulates, Lorentz transformations, time dilation, Minkowski diagrams, Doppler effect - Covariant formulation of classical mechanics and electomagnetism, force, momentum and velocity 4 vectors, particle dynamics and collisions, Maxwell tensor, Lorentz transformations of electric and magnetic fields.
 Pre-requisites Students MUST have passed: Mathematics for Physics 4 (PHYS08038) AND ( Mathematics for Physics 3 (PHYS08037) OR Dynamics and Vector Calculus (PHYS08043)) Co-requisites Prohibited Combinations Students MUST NOT also be taking Electromagnetism and Relativity (PHYS10093) Other requirements None
 Pre-requisites None
 Academic year 2014/15, Available to all students (SV1) Quota:  None Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 37, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 61 ) Assessment (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 % Additional Information (Assessment) 100% Examination Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) 2:00
 Upon successful completion of this course it is intended that a student will be able to: 1. be confident with the index notation and the Einstein summation convention 2. have a good working knowledge of matrices and determinants and be able to derive vector identities 3. understand the meaning and significance of rotational symmetry and its application to simple physical situations 4. be confident with the generalisation to non-orthogonal co-ordinate systems and the subsequent covariant and contravariant tensors 5. understand the foundations of special relativity and the consequences of a constant speed of light 6. have a working knowledge of relativistic particle mechanics 7. understand the implications for electromagnetism. 8. to be able to apply what has been learned in the course to solving new problems
 None
 Graduate Attributes and Skills Not entered Keywords SCM
 Course organiser Dr Roger Horsley Tel: (0131 6)50 6481 Email: rhorsley@ph.ed.ac.uk Course secretary Mrs Bonnie Macmillan Tel: (0131 6)50 5905 Email: Bonnie.MacMillan@ed.ac.uk
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