Undergraduate Course: Physical Mathematics (PHYS09052)
|School||School of Physics and Astronomy
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 9 (Year 3 Undergraduate)
|Home subject area||Undergraduate (School of Physics and Astronomy)
||Other subject area||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)
||Other requirements|| None
|Additional Costs|| None
Information for Visiting Students
|Displayed in Visiting Students Prospectus?||No
Course Delivery Information
|Not being delivered|
Summary of Intended Learning Outcomes
|Details to follow.
|Coursework 20%, examination 80%.|
||- 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.
||Course secretary||Miss Jillian Bainbridge
Tel: (0131 6)50 7218