MTH1035 - Techniques for modelling (advanced)

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Overview

Solution of systems of linear equations using Gaussian elimination; matrices and determinants, eigenvalues and eigenvectors; introduction to vectors; parametric curves; 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 … For more content click the Read More button below.

Solution of systems of linear equations using Gaussian elimination; matrices and determinants, eigenvalues and eigenvectors; introduction to vectors; parametric curves; 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; Sequences and series, Taylor series and series convergence, the remainder term.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Burkard Polster

Unit Coordinator(s)

Dr Andy Hammerlindl

Learning outcomes

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

Understand the basic concepts of linear algebra, and 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;

Understand the concept of mathematical proof and the difference between proof by construction and proof by induction;

10.

Prove elementary theorems by induction and by construction.

Assessment

1 - Continuous assessment

2 - Examination (2 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workload requirements

Workload

Learning resources

Required resources

Technology 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

Applied mathematics
Astrophysics
Atmospheric science
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics