•Modelling of environmental systems, through conceptual models showing linkages of variables, and full mathematical models. Using discrete and continuous models of biological, chemical and physical processes, the ecology and physical behaviour of environmental systems is represented by models with analytic or numerical solutions. A range of mathematical methods including: analytic and approximate methods (through spreadsheets) for ordinary differential equations, Fourier series solutions for partial differential equations, matrix models and simple difference equations; elementary systems analysis; are used to explore models, and their use in depicting the behaviour of simple physical systems.
•- Introduction and overview of modelling, empirical, dimensional analysis, ordinary differential equations (ODE’s). - Population like models, development of terms, Von Bertalanffy fish model, Bernoulli differential equations (DE’s). - Numerical methods for ODE’s: Euler’s method, Runge-Kutta methods. - Systems of ODE’s: analytical and numerical solution, decomposition of high order DE’s. - Markov chains, classification and long-run behavior. - Time Series, Markov annual stream flow. - Modelling with partial differential equations (PDE’s), directly integrable, advection and method of characteristics. - Method of separation of variables, Fourier series, Euler’s formulas. - Dirichlet, Gibbs and Parseval phenomenon, odd and even extensions. - Diffusion equation with numerical methods. - Wave equation with numerical methods. |
| | Learning Outcomes Assessed | Assessment Tasks | Assessment Type | Weighting | | 1. | K1, S1 - S4, A1, A2 | Problem solving and modelling techniques, analyticaland numericalsolution ofmodels involvingordinary and partial differential equations,use of software, appliedmatrix methods,time series analysis. | Written assignments | 30% - 50% | | 2. | K1, S1 - S4, A1, A2 | Demonstrateknowledge of solution and interpretation of mathematical models. | Written examination | 50% - 70% |
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