This module MA90143: Applied Differential Equations has three main units described below:
- Applied ordinary differential equations: Series solution of linear ordinary differential equations with variable coefficients, special functions, boundary value problems, Green's functions, phase diagrams and stability.
- Partial differential equations: Quasi-linear partial differential equations of 2nd order, Classifications and reduction to canonical form, method of separation of variables (MSV)/Fourier method
- Initial and Boundary Values Problems (IVP and BVP) for Equations of Mathematical Physics: wave equation for infinite string (D’Alembert formula), wave equation in for finite string, heat equation for finite rod and Laplace's equation ( Dirichlet, Neumann and Dirichlet-Neumann BVP) in Cartesian and cylindrical coordinates.
The module is designed to provide students with an advanced understanding of algebraic structures, with particular emphasis on non-associative algebras and their applications in geometry. It covers selected algebraic systems, including symmetric, dihedral, and quaternion groups, as well as quasigroups and loops, with further attention to the concepts of isotopy and parastrophy in quasigroups. The module also examines modules over a ring as a generalization of vector spaces in which scalars are drawn from a ring rather than a field. Topics in this area include left and right modules, submodules, module homomorphisms, quotient modules and isomorphism theorems, direct sums and products, injective and projective modules, free modules, finitely generated and Noetherian modules, exact sequences, module decomposition, and tensor products. In addition, the module considers pedagogical approaches for enhancing the teaching and learning of algebra across different levels of education.
The aim of the module is to equip students with skills in dealing with real data using various statistical data analysis tools. This module introduces students to a range of multivariate statistical methods used in research and available in the statistical packages such as SPSS, Stata, and R. The emphasis will be on the use of statistics and probability in interpreting research data in the field of Mathematics education.