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

Advanced calculus is fundamental to the study of applied mathematics and related quantitative disciplines such as physics, physical chemistry and engineering. In order to succeed in these and related fields you will need a strong grounding in advanced calculus techniques and theory.

Aims

This postgraduate unit will endeavour to introduce you to new skills and methodologies that are essential to the study of science, technology and engineering. It will also provide the necessary background for those of you who go on to more advanced study in mathematics.

Objectives

Successful completion of this unit should enable you to:

1. Demonstrate a knowledge of the basic mathematical theory of differential and integral calculus for functions of 2 or more variables defined explicitly and implicitly.
2. Apply calculus techniques to determine series approximations and extrema in an unconstrained and constrained setting, for functions of 2 or more variables.
3. Demonstrate a knowledge of the mathematical theory of vector fields and apply calculus techniques to such fields including the development of versions of the Fundamental Theorem of Calculus for integrals of vector fields.
4. Draw on a range of knowledge and thinking skills to solve problems.
5. Decompose a problem into smaller parts, solve these and hence solve the original problem setting out calculations clearly and using consistent mathematical notation.

Content

Multivariable calculus: multivariable functions, limits and continuity, partial derivatives, higher-order derivatives, the chain rule, linear approximations and differentiability, differentials, gradients and directional derivatives, implicit functions, Taylor series and approximations, extreme values, double integrals, triple integrals, change of variables in multiple integrals, applications of multiple integrals.

Vector calculus: vector and scalar fields, conservative fields, line integrals, surfaces and surface integrals, oriented surfaces and flux integrals, gradient, divergence and curl.

Approaches to Teaching and Learning

You are expected to attend lectures (3 hours per week) in which the course content will be introduced and the associated skills will be demonstrated. You will have the opportunity in lectures to practise these skills. A combination of discussions, working on problems and presenting solutions will promote creativity in problem solving, critical assessment skills and intellectual debate. You should also attend and contribute to tutorial sessions (1 hour per week) which will involve further learning exercises with a greater opportunity for individual attention and assistance if you need it.

This unit is being taught concurrently with an undergraduate offering of the same subject. University policy permits that postgraduate and undergraduate students attend the same lectures. Separate tutorial/discussion groups will be provided for postgraduate student where numbers allow. As a postgraduate student you will be required to complete separate or additional assessment.

Assessment

All assessment contributes to your grade.Feedback will be available on your progress.

Assessment name: Problem Solving Task
Description: (Formative and summative) - (Mark: M1) In Week 7 of semester, you will have the opportunity to hand in your solutions to a number of problems that arise from the material presented in the lectures during the first 5 weeks of semester. Weight: 40% maximum.
Relates to objectives: 1 to 5.
Weight: 40%
Internal or external: Internal
Group or individual: Individual
Due date: Week 7

Assessment name: Examination (Theory)
Description: (Mark: (M2+M3)). At the end of the semester, you will sit a final examination paper of 3 hours duration. This paper will be comprised of two sections, Part A (mark M2) worth 40% of the total marks and Part B (mark M3) worth 60% of the total marks allocated on the paper. The material examined in the Part A section will correspond to the material examined in the problem solving task. The material examined in Part B will be drawn from the lecture topics covered in weeks 6 to 13 of semester.
Your final mark for the unit = MAX[M1, M2] + M3. Weight: 60% minimum.
Relates to objectives: 1 to 5.
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: End 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

Texts:

There is no prescribed text for this unit.

References:

1. Adams RA & Essex C (2010) Calculus: a Complete Course, 7th edition, Pearson Education Canada Inc

2. Anton H, Bivens I & Davis S (2002) Calculus: Early Transcendentals, 7th edition, John Wiley & Sons Inc

3. Kaplan W (2003) Advanced Calculus, 5th edition, Addison-Wesley Higher Mathematics

Risk assessment statement

There are no out of the ordinary risks associated with this unit. You will be informed of evacuation procedures and assemble areas in the first few lectures. More information on health and safety can be found at http://www.hrd.qut.edu.au/healthsafety/

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: 19-Oct-2012