# ENV2792 - Mathematical models of the environment - 2018

## 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.

Faculty

Engineering

Chief examiner(s)

Coordinator(s)

Not offered in 2018

Prerequisites

MTH1085 or equivalent, ENV1711

## 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%

3 hours of lectures, 2 hours of tutorials/PC laboratories and 7 hours of private study per week