MTH1030 - Techniques for modelling

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Overview

Solution of systems of linear equations using Gaussian elimination; matrices, determinants, eigenvalues and eigenvectors; introduction to vectors; methods of integration - substitutions and integration by parts; solution of first-order ordinary differential equations - separable, use of integrating factor; solution of second-order linear ordinary differential equations with constant coefficients and applications; … For more content click the Read More button below.

Solution of systems of linear equations using Gaussian elimination; matrices, determinants, eigenvalues and eigenvectors; introduction to vectors; methods of integration - substitutions and integration by parts; solution of first-order ordinary differential equations - separable, use of integrating factor; solution of second-order linear ordinary differential equations with constant coefficients and applications; Taylor series and series convergence; the remainder term.

Offerings

S1-01-CLAYTON-ON-CAMPUS

S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

PREREQUISITE: You must have passed MTH1020 with a mark of at least 60 or VCE Specialist Mathematics units 3 and 4 with a raw study score of at least 30. Exceptions for students who passed MTH1020 with a mark in the range of 50 to 59 can be made with permission from the unit coordinator based on a diagnostic test. If you enrol in this unit and do not meet one of these prerequisites you will be discontinued.

PROHIBITION: ENG1005, ENG1091, MTH1035

Contacts

Chief Examiner(s)

Associate Professor Burkard Polster

Unit Coordinator(s)

Associate Professor Burkard Polster

Dr Gregory Markowsky

Learning outcomes

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

Understand the basic concepts of linear algebra, recognise and manipulate elements of vector spaces;

Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;

Identify and evaluate improper integrals;

Solve simple first and second order differential equations, and formulate them for applications to physical systems;

Compute Taylor series expansions, with remainder, for functions of one variable;

Apply Taylor series and l'Hopital's rule to compute limits;

Understand and compute the convergence properties of infinite series;

Provide written reports that contain complete mathematical arguments.

Teaching approach

Active learning

Assessment

1 - Continuous assessment

2 - Examination (2 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (Unit course reader, Printing, Stationery)- $120.

Availability in areas of study

This unit applies to the following courses:
Applied mathematics
Astrophysics
Atmospheric science
Computational science
Financial and insurance mathematics
Mathematical statistics
Mathematics
Physics
Pure mathematics