Units

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Sample subject outline - Semester 1 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

Building upon the foundations established in MAB125 or Senior Maths C, this unit addresses the significant role of mathematical modelling using vectors, matrices and multivariable calculus for the description and resolution of simple and complex problems relevant to the discipline of engineering. The formulation and solution of such problems is supported by appropriate advanced mathematical concepts used for function approximation, differentiation and integration. You will complete this unit in first year or first semester of second year depending on your initial maths background.

Aims

Undertaking this unit will allow you to develop your problem solving skills, especially in the context of mathematical techniques related to multivariable functions, vectors and matrices used to model engineering relevant problems.

Objectives

Successful completion of this unit will enable you to:

1. Demonstrate competency in the use and interpretation of mathematical notation.
2. Recognise, interpret and solve problems formulated with multiple independent variables.
3. Apply matrix and vector methods to engineering related problems and interpret their solution.
4. Demonstrate your ability to reduce complex problems to smaller elements.

Content

Multivariable calculus is introduced in this unit leading to the exploration of ideas such as level curves, partial derivatives, directional derivatives, gradient, tangent planes, implicit differentiation and the integration of multivariable functions. Applications may include the determination of extrema, the use of differentials for estimating functions and calculating volumes and other properties of 3 dimensional bodies.

Vector calculus is introduced in this unit by considering vector equations of lines, planes and curves. Applications may include the determination of arc length, projectile motion problems, and the use of polar coordinates.

Linear Algebra: This unit introduces vector and matrix methods. The concepts and problems covered include:vectors and matrix operations, solution of systems of linear equations, transpose and inverse of a matrix, determinants, diagonal, triangular and symmetric matrices, norm of a vector, dot product, cross product, orthogonality, lines and planes in 3-space, eigenvalues and eigenvectors.

Approaches to Teaching and Learning

Lectures: 3 hr/wk
Practicals: 1 hr/wk

You are expected to undertake lectures in which the unit content will be introduced and the associated skills will be demonstrated and discussed. You should also attend and participate in practical sessions, designed to reiterate key elements of content and to provide you with directed assistance to develop your competency in the techniques required.

Participation in the voluntary Mathematics Access Centre support sessions is recommended for those students needing additional specific learning support.

Lecture, practical, homework and other resources are provided via Blackboard and all students are strongly encouraged to make use of these.

Assessment

General Assessment Information
The assessment items in this unit are designed to determine your level of competency, measured against criteria, in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.Feedback to students
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.

Summative feedback will be provided throughout the semester with progressive posting of results via Blackboard.

Assessment name: Problem Solving Tasks
Description: Exposition of techniques and problem solving, with a distribution of long and short answers required. Will include online and written problem solving.
Relates to objectives: Relates to learning outcomes:1, 2, 3 and 4.
Weight: 40%
Internal or external: Internal
Group or individual: Individual
Due date: Throughout Semester

Assessment name: Examination
Description: Exposition of techniques and problem solving with a distribution of short and long answers required.
Relates to objectives: Relates to learning outcomes:1, 2, 3 and 4.
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: End of Semester

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

There are no prescribed textbooks. Notes and resources will be provided online during the semester.

The following are optional textbooks that cover the material in this unit.

The textbook recommended for the topics in multivariable calculus and vector calculus is:
Anton, Bivens and Davis (2012): Calculus: early transcendentals. International Student Version. Combined 10th edition. (Binder ready version or hardcover) [earlier editions are fine, too]

The textbook recommended for the topics in linear algebra is:
Anton, Rorres (2010): Elementary Linear Algebra: Applications Version, 10th Edition. [earlier editions are fine, too]

Risk assessment statement

There are no out of the ordinary risks associated with this unit since lectures and practicals are held in ordinary lecture theatres or computer laboratories. Basic safety procedures in computer laboratories will be given to you when entering the computer laboratory for the first time. In addition, emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the university's health and safety website for further information.

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 18-Oct-2012