Unit Guide

General Information

Unit convenor and teaching staff	Unit convenor and teaching staff Paul Bryan paul.bryan@mq.edu.au Ross Moore ross.moore@mq.edu.au
Credit points	Credit points 10
Prerequisites	Prerequisites MATH2010 or MATH2055 or MATH235
Corequisites	Corequisites
Co-badged status	Co-badged status
Unit description	Unit description The topics covered in this unit lay the foundations for further study in modern areas of mathematics (such as partial differential equations, fluid mechanics, and mathematical biology). This unit builds on the first year single variable calculus units by extending calculus to several variables, and focuses primarily on integration techniques for complex functions and vector fields. Complex analysis is the study of complex-valued functions of complex variables. The main properties of complex functions of a single complex variable will be presented, including the important concepts of analyticity and singularity structure. This will be followed by a treatment of Cauchy's theorem and the residue theorem to evaluate contour integrals of complex functions around various curves in the complex plane. Vector calculus is the study of vector fields in two and three dimensions, and facilitates the modelling of a variety of physical phenomena, for example in fluid mechanics and electromagnetism. By introducing the gradient, divergence and curl operators, the main properties of vector fields can be analysed. A variety of integrals of vector fields over paths, surfaces and volumes will be performed, and the application of three important integral theorems of vector calculus due to Green, Stokes and Gauss to evaluate these integrals will be demonstrated.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates

Learning Outcomes

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

ULO1: Analyse the main properties of functions of a single complex variable, such as analyticity and singularity structure.
ULO2: Evaluate contour integrals of complex functions by applying Cauchy's theorem and the residue theorem.
ULO3: Analyse the main properties of vector fields using the gradient, divergence and curl operators.
ULO4: Evaluate path, surface and volume integrals of vector fields.
ULO5: Apply the important theorems due to Green, Stokes and Gauss to physical applications.

General Assessment Information

Late Assessment Submission Penalty

From 1 July 2022, Students enrolled in Session based units with written assessments will have the following late penalty applied. Please see https://students.mq.edu.au/study/assessment-exams/assessments for more information.

Unless a Special Consideration request has been submitted and approved, a 5% penalty (of the total possible mark) will be applied each day a written assessment is not submitted, up until the 7th day (including weekends). After the 7th day, a grade of '0' will be awarded even if the assessment is submitted. Submission time for all written assessments is set at 11:55 pm. A 1-hour grace period is provided to students who experience a technical concern.

For any late submission of time-sensitive tasks, such as scheduled tests/exams, performance assessments/presentations, and/or scheduled practical assessments/labs, students need to submit an application for Special Consideration.

Assessments where Late Submissions will be accepted

In this unit, late submissions will be accepted as follows:

Assignment 1, Assignment 2 – YES, Standard Late Penalty applies Test 1, Test 2, Final Exam - NO, unless Special Consideration is granted

Assessment Tasks

Name	Weighting	Hurdle	Due
Test 2 (Online)	15%	No	Week 10
Final exam	50%	No	Examination Period
Assignment 2	10%	No	Week 12
Assignment 1	10%	No	Week 7
Test 1 (Online)	15%	No	Week 4

Test 2 (Online)

Assessment Type ¹: Quiz/Test
Indicative Time on Task ²: 10 hours
Due: Week 10
Weighting: 15%

Online test