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)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | 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 non-uniform random numbers.
- Addition of random variables as a convolution; addition of Gaussian distributions; central-limit 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; Kolmogorov-Smirnov 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 |
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