This subject aims to equip students with the mathematical methods used to solve ordinary and partial differential equations, which occur in modelling engineering systems, and to carry out calculations with basic error-correcting codes.
Error-correcting codes.
Review of matrices and modular arithmetic. Linear block codes. Generator and parity-check matrices. Hamming distance. Error detection and correction capabilities. Cosets. Syndrome. Decoding table. Single error-correction and Hamming codes.
Functions of a complex variable.
Differentiability and the Cauchy-Riemann equations. Contour Integrals. Cauchy's Theorem. Cauchy's Integral Formula. Taylor and Laurent series. Singularities and Poles. Residues and their calculation. Cauchy's Theorem. Residue Theorem and Applications.
Ordinary Differential equations.
General and particular solutions. Initial value and boundary value problems. Integrating Factor Method. Bernouilli Equation. Laplace transform technique. Systems of linear differential equations. Loop currents. Legendre and Bessel’s equation. Series solutions.
Partial Differential Equations.
Second-order linear partial differential equations. Elliptic, hyperbolic and parabolic PDE’s. The Wave Equation. d’Alembert’s solution. Vibrating string. Diffusion equation. Separation of variables. Applications to transmission lines. Laplace's equation. Poisson’s equation.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 20 |
| Formal Examination | 80 |