[1-6] Fourier Series and Fourier Transforms. Comparison of time and frequency domain. Fourier transforms and inverse transforms. Convolution. Application to signal processing. Quick method for calculating Fourier transforms.
[7-8] Probability. Meaning of probability. Dependent, independent and mutually exclusive events.
[9-12] Statistics. Definition of terms. The probability density function. Normalisation. Normal, Binomial and Poisson probability density functions. Applications to errors, noise, and least squares fitting of straight lines and other curves to data.
[13-15] Method of least squares.
[16-18] Matrices. Determinants. Matrix algebra. Transpose and inverse. Solution of linear simultaneous equations. Eigenvalues and eigenvectors. Two-port parameters.
[19-22] Vectors. Sum, scalar product, dot product, cross product. Vector differential operators: grad, div, curl. Applications and interpretation.
[23-24] The wave equation. Derivation and d'Alembert solution.
[25-30]
Laplace
transforms. Complex frequency. Partial fractions and the solution of differential equations by
Laplace
transform. Mechanical examples as well as electronic ones.
[31-38] Z-transforms. Definition, propertires, inversion. Applications and worked examples.
[39-40] Cross- and Autocorrelation. Definition, examples, applications.
[41-42] Revision. Topics covered to be selected by the students.
