MTH2040 - Mathematical modelling

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Overview

The mathematical modelling of physical systems is based upon differential equations and linear algebra. This unit will introduce fundamental techniques for studying linear systems and differential equations, focusing on applications to physical systems. The topics in linear algebra to be considered include eigenvalues and eigenvectors, diagonalisation of square matrices, matrix functions, LU-decomposition, applications. The topics in optimisation include Lagrange multipliers, the method of least-squares, linear programming, applications. Finally, the topics in differential equations include matrix solutions of constant coefficient systems of ordinary differential equations, conservative systems and phase-planes of simple non-linear ordinary differential equations. Solutions of first order partial differential equations will be analysed and applied to real world problems. You will be introduced to the Mathematica computer package, and learn how to use it for analytical and numerical calculations and graphics. Mathematica will be integrated into most activities.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Requisites

Prerequisite

Prohibition

Contacts

Chief Examiner(s)

Professor Paul Cally

Unit Coordinator(s)

Professor Paul Cally

Dr Alina Donea

Learning outcomes

On successful completion of this unit, you should be able to:

Apply differential equations and linear algebra to the modelling of real-world systems;

Solve linear systems and calculate the eigenvalues and eigenvectors of square matrices;

Calculate the solution of difference and differential equations using matrix functions;

Apply optimisation techniques to the solution of real-world problems;

Solve constant coefficient ordinary differential equations;

Apply the Method of Characteristics to the solution to first order differential equations;

Understand the phase-planes for second-order differential equations describing oscillating systems and interacting populations.

Use the Mathematica software package for the solution and presentation of mathematical problems.

Present clear mathematical arguments in both written and oral forms.

Teaching approach

Active learning

Assessment

1 - In-semester assessment

2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workload requirements

Workload

Learning resources

Required resources

Other unit costs

Costs are indicative and subject to change.
Miscellaneous Items Required (Unit Course Reader, Printing, Stationery) - $120.

Availability in areas of study

Astrophysics
Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Physics
Pure mathematics