units

ENV2792

Faculty of Engineering

# Undergraduate - UnitENV2792 - Mathematical models of the environment

This unit entry is for students who completed this unit in 2015 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study. print version

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

 Level Undergraduate Faculty Faculty of Engineering Offered Not offered in 2015 Coordinator(s) Dr John Arkinstall

### Synopsis

This unit introduces the 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.

### Outcomes

On completion of this unit, students will be able to produce a concise conceptual map of an environmental system, as an aid in formulating a mathematical model representing the system; be able to formulate conceptual and mathematical models in ecological, environmental and physical contexts; be able to examine a simple mathematical model of an environmental system, in order to describe its assumptions and to investigate and interpret its predictions; be familiar with several types of models such as: mass balance, input-output, multi-compartment, equilibrium, competition models; illustrated by specific models representing physical and ecological phenomena such as rainfall, evapotranspiration, energy cycles, population growth , chemical reactions, air and plume flow, spatial variability, oscillation, feedback etc; be able to manipulate and solve a variety of simple mathematical models of environmental systems; be able to use spreadsheets and other appropriate software to implement and investigate the solutions of several types of models; be able to apply the following techniques to environmental models: analytic solution of simple 1st and 2nd order ordinary differential equations; solving the one dimensional heat and wave equations, solving analytically linear difference equations in one variable, and linear matrix/vector evolution equations

### Assessment

Assignments: 40%
Examination (3 hours): 60% 