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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014
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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

Undergraduate Course: Mathematics for Physics 3 (PHYS08037)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) Credits20
Home subject areaUndergraduate (School of Physics and Astronomy) Other subject areaNone
Course website WebCT Taught in Gaelic?No
Course description*** Course discontinued as of 2012/13***

This course is designed for pre-honours physics students, to learn linear algebra, multivariate calculus, and the use of simple differential equations to describe basic concepts in physics. The course consists of an equal balance between lectures to present new material, and workshops to develop understanding, familiarity and fluency.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Physics 1A: Foundations (PHYS08016) AND ( Mathematics for Physics 1 (PHYS08035) AND Mathematics for Physics 2 (PHYS08036)) OR ( Practical Calculus (MATH08001) AND Solving Equations (MATH08002) AND Geometry & Convergence (MATH08003) AND Group Theory: An Introduction to Abstract Mathematics (MATH08004))
Co-requisites Students MUST also take: Physics 2A (PHYS08022) OR Accelerated Algebra and Calculus for Direct Entry (MATH08062)
Prohibited Combinations Students MUST NOT also be taking Dynamics (PHYS08040)
Other requirements For Fast Track students: SCE Advanced Higher or A Level Physics and Mathematics at A Grade or equivalent.
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?No
Course Delivery Information
Not being delivered
Summary of Intended Learning Outcomes
On completion of this course it is intended that student will be able to
Demonstrate understanding and work with real vector spaces, vector products, and expansion in an orthonormal basis, and apply to static problems from classical mechanics.
Demonstrate understanding and work with matrices including inverses, determinants, and diagonalization, and apply these in static mechanics (eg stress and strain).
Demonstrate understanding and work with complex vectors, hermitian and unitary matrices, and apply these to simple examples in quantum mechanics (eg two state systems)
Demonstrate understanding and work with multivariate calculus: the chain rule, Taylor expansions, maxima, minima and saddles, polar co-ordinates, with usual physics examples (eg stability), and planar and volume integrals.
Demonstrate understanding and work with ordinary differential equations, homogenous and inhomogeneous, first order and second order, the harmonic oscillator (free, damped and forced), with examples from classical mechanics.
Demonstrate understanding of energy, momentum and angular momentum conservation, and apply them to central force problems.
Demonstrate understanding and work with coupled oscillators and expansion in normal modes, with examples from classical mechanics and quantum mechanics.
Assessment Information
20% coursework
80% examination
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus Statics
1. real vectors, bases, orthogonality, expansion in basis, change of basis, dot and cross products, scalar and vector triple products, all with examples from classical mechanics and electrostatics; matrices and matrix algebra, rank, inverse, determinants, eigenvalues and eigenvectors, diagonalization, applications in mechanics (possibly coupled oscillators); complex vectors, hermitian and unitary matrices, simple examples in quantum mechanics;
2. Elementary multivariate calculus; partial derivatives, chain rule, Taylor expansions, maxima, minima and saddles, polar co-ordinates, with usual physics examples; planar integrals and volume integrals;

Dynamics
1. ordinary differential equations, homogenous and inhomogeneous, first order, integrating factor, second order, harmonic oscillator (free, damped and forced), solution by series, with examples from classical mechanics. Angular momentum, conservation, orbits for central forces. Coupled oscillators, normal modes.
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
KeywordsMfP3
Contacts
Course organiserDr Brian Pendleton
Tel: (0131 6)50 5241
Email: b.pendleton@ed.ac.uk
Course secretaryMiss Jillian Bainbridge
Tel: (0131 6)50 7218
Email: J.Bainbridge@ed.ac.uk
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