Undergraduate Course: Mathematics for Physics 4 (PHYS08038)
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 the techniques of vector calculus, Fourier series and transforms, and simple partial 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 vector fields and the basic operations of vector calculus, and apply these to a range of problems from of heat flow, fluid flow, electrostatics, and potential theory.
¿ Demonstrate understanding and work with line, surface and volume integrals, and the associated theorems of Green, Stokes and Gauss, and to apply these to physical problems, for example, fluid flow, heat flow and electromagnetism.
¿ Demonstrate understanding and work with Fourier series and complex functions, their applications to the solution of ordinary differential equations and elementary physical examples such as standing waves.
¿ Demonstrate understanding of the Fourier Transform, inversion formula, convolution and Parseval's theorem. To apply these to a range of physical situations, for example, harmonic oscillators and travelling waves, and understand the link to the uncertainty principle.
¿ Demonstrate understanding of the use of linear response functions, their relation to convolution and associated delta and Green's functions, and to apply these to inhomogenous static and dynamical problems (Poisson and sources of waves).

Assessment Information
20% coursework
80% examination 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
Fields
1. vector fields, grad, div and curl, the Laplacian, identities, potential theorems, polar coordinates, Laplace and Poisson equations, boundary value problems, with examples from fluid flow, heat flow, electrostatics;
2. Line, surface and volume integrals, and evaluation thereof in rectangular and polar coordinates, integral theorems (Green, Gauss & Stokes), conservation laws (mass in fluids, charge in electromagnetism, circulation around closed curves in fluids).
Waves
1. Fourier Series: complex fns, Fouriers Thm, determining coefficients, solving ODEs with Fourier series, linear algebra view, simple physics examples in terms of standing waves, bound states;
2. Fourier Transform: inversion formula, convolution, Parseval, uncertainty principle, forced damped harmonic oscillator, expansion of solutions, travelling waves;
3. Linear response (and reln to convolution thm), delta function and Greens functions (Poisson and Waves). 
Transferable skills 
Not entered 
Reading list 
Not entered 
Study Abroad 
Not entered 
Study Pattern 
Not entered 
Keywords  MfP4 
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 

