Undergraduate Course: Mathematics for Physics 3 (PHYS08037)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Credits  20 
Home subject area  Undergraduate (School of Physics and Astronomy) 
Other subject area  None 
Course website 
WebCT 
Taught in Gaelic?  No 
Course description  *** Course discontinued as of 2012/13***
This course is designed for prehonours 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. 
Information for Visiting Students
Prerequisites  None 
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 coordinates, 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 coordinates, 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 
Keywords  MfP3 
Contacts
Course organiser  Dr Brian Pendleton
Tel: (0131 6)50 5241
Email: b.pendleton@ed.ac.uk 
Course secretary  Miss Jillian Bainbridge
Tel: (0131 6)50 7218
Email: J.Bainbridge@ed.ac.uk 

