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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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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)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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.
Entry Requirements (not applicable to Visiting Students)
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
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Academic year 2015/16, 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
Learning Outcomes
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
Reading List
None
Additional Information
Graduate Attributes and Skills Not entered
KeywordsSCM
Contacts
Course organiserDr Roger Horsley
Tel: (0131 6)50 6481
Email:
Course secretaryMrs Bonnie Macmillan
Tel: (0131 6)50 5905
Email:
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