This module is divided into two sections. The first section introduces the learner to vector calculus and line integrals. The concepts and methods of Fourier analysis are covered and applied by way of example. The second section covers random variables and examines some of the more popular probability distributions .The learner is introduced to the statistical techniques of hypothesis testing and regression and correlation.
Fourier series, sine and cosine form leading to exponential form. Introduction to Fourier transform- properties, including scaling, modulation and frequency shifting. Parseval’s Theorem, energy conservation and energy spectra .Dirac delta function, impulse response. Transforms of square, pulse, triangular waveforms.
Determinants. Eigenvalues and Eigenvectors. Diagonalisation of a matrix. Applications to systems of differential equations. Orthogonal matrices. Applications to physics problems.
Probability mass functions. Expected values and variances. The binomial, Poisson and geometric distributions. Probability density functions. The uniform, normal and exponential distributions.
Null and alternative hypotheses. Types I and II errors. Z and t tests for single sample and two sample, paired and unpaired data.
Regression and Correlation
Simple linear regression. Estimation of parameters. Coefficient of determination and correlation coefficient
Lectures supported by tutorials and problem sheets which may be supplemented by online materials and the use of mathematical software packages.
|Module Content & Assessment