Undergraduate Course: Physical Mathematics (PHYS09052)
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 9 (Year 3 Undergraduate) 
Credits  10 
Home subject area  Undergraduate (School of Physics and Astronomy) 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  *** This course is no longer running ****
Details to follow  second half of the proposed Fourier Analysis and Statistics course. 
Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Additional Costs  None 
Information for Visiting Students
Prerequisites  None 
Displayed in Visiting Students Prospectus?  No 
Course Delivery Information
Not being delivered 
Summary of Intended Learning Outcomes
Details to follow. 
Assessment Information
Coursework 20%, examination 80%. 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
 Overview of Partial Differential Equations in Physics: Poisson, Wave, Diffusion, Continuity, Laplace, Schrodinger.
 Separation of variables.
 Examples with rectangular symmetry: `'rectangular harmonics'.
 Examples with circular symmetry: Bessel functions.
 Examples with spherical symmetry: Legendre polynomials, spherical harmonics; Charged sphere, gravitational potential.
 Probability of discrete events; Multiple events: joint, conditional and marginal distributions.
 Bayes' theorem; frequentist view; probability as a degree of belief.
 Generalisation of probability to continuous variables.
 Permutations, combinations.
 Random walk and the binomial distribution; Stirling's approximation;
Gaussian and Poisson distributions as limiting cases.
 Functions of a random variable: expectations, moments; Fourier transform of probability distribution as moment generating function;
Application to sampling nonuniform random numbers.
 Addition of random variables as a convolution; addition of Gaussian distributions; centrallimit theorem.
 Estimating mean, variance, error on the mean from finite data sets.
 Cumulative distribution and centiles; error function; hypothesis testing, confidence limits.
 Least squares fitting; goodness of fit; x2 distribution; maximum likelihood; improbably good and poor fits.
 Residuals; error analysis; KolmogorovSmirnov test.
 Linear regression; correlations. 
Transferable skills 
Not entered 
Reading list 
Not entered 
Study Abroad 
Not entered 
Study Pattern 
Not entered 
Keywords  PMath 
Contacts
Course organiser  
Course secretary  Miss Jillian Bainbridge
Tel: (0131 6)50 7218
Email: J.Bainbridge@ed.ac.uk 

