Students
MATH2020 – Vector Calculus and Complex Analysis
2025 – Session 2, In person-scheduled-weekday, North Ryde
General Information
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| Unit convenor and teaching staff |
Unit convenor and teaching staff
Lecturer
Frank Valckenborgh
Contact via via email
12WW 613
Lecturer
Paul Bryan
Contact via via email
12WW 706
|
|---|---|
| Credit points |
Credit points
10
|
| Prerequisites |
Prerequisites
MATH2010 or MATH2055
|
| 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
Requirements to Pass this Unit
To pass this unit you need to achieve a total mark equal to or greater than 50% across all assessments.
Attendance and participation
We strongly encourage all students to actively participate in all learning activities. Regular engagement is crucial for your success in this unit, as these activities provide opportunities to deepen your understanding of the material, collaborate with peers, and receive valuable feedback from instructors, to assist in completing the unit assessments. Your active participation not only enhances your own learning experience but also contributes to a vibrant and dynamic learning environment for everyone.
Late Assessment Submission Penalty
The submission time for all uploaded assessments is 11:55 pm. A 1-hour grace period will be provided to students who experience a technical concern.
For any late submission of time-sensitive tasks, such as scheduled tests/exams, assignments, performance assessments/presentations, and/or scheduled practical assessments/labs, please apply for Special Consideration: https://connect.mq.edu.au.
Late Submissions will be accepted only if Special Consideration is Granted.
Special Consideration
The Special Consideration Policy aims to support students who have been impacted by short-term circumstances or events that are serious, unavoidable and significantly disruptive, and which may affect their performance in assessment. If you experience circumstances or events that affect your ability to complete the assessments in this unit on time, please inform the convenor and submit a Special Consideration request through https://connect.mq.edu.au.
Written Assessments/Quizzes/Tests: If you experience circumstances or events that affect your ability to complete the written assessments in this unit on time, please inform the convenor and submit a Special Consideration request through https://connect.mq.edu.au.
Assessment Tasks
| Name | Weighting | Hurdle | Due |
|---|---|---|---|
| Skills exercise | 25% | No | 11:55pm 14 September 2025 |
| Assignment | 25% | No | 11:55pm 2 November 2025 |
| Final examination | 50% | No | Exam Period |
Skills exercise
Assessment Type 1: Practice-based task
Indicative Time on Task 2: 15 hours
Due: 11:55pm 14 September 2025
Weighting: 25%
Exercises designed to develop and assess mathematical skills, reinforcing theoretical knowledge to promote mastery of essential concepts.
On successful completion you will be able to:
- Analyse the main properties of functions of a single complex variable, such as analyticity and singularity structure.
- Evaluate contour integrals of complex functions by applying Cauchy's theorem and the residue theorem.
- Analyse the main properties of vector fields using the gradient, divergence and curl operators.
- Evaluate path, surface and volume integrals of vector fields.
- Apply the important theorems due to Green, Stokes and Gauss to physical applications.
Assignment
Assessment Type 1: Problem set
Indicative Time on Task 2: 15 hours
Due: 11:55pm 2 November 2025
Weighting: 25%
The assignment will test the ability of students to apply mathematical concepts and techniques to problem solving and includes a report building on a covered topic.
On successful completion you will be able to:
- Analyse the main properties of functions of a single complex variable, such as analyticity and singularity structure.
- Evaluate contour integrals of complex functions by applying Cauchy's theorem and the residue theorem.
- Analyse the main properties of vector fields using the gradient, divergence and curl operators.
- Evaluate path, surface and volume integrals of vector fields.
- Apply the important theorems due to Green, Stokes and Gauss to physical applications.
Final examination
Assessment Type 1: Examination
Indicative Time on Task 2: 20 hours
Due: Exam Period
Weighting: 50%
The exam will test the ability of students to utilise concepts and techniques learnt in the unit.
On successful completion you will be able to:
- Analyse the main properties of functions of a single complex variable, such as analyticity and singularity structure.
- Evaluate contour integrals of complex functions by applying Cauchy's theorem and the residue theorem.
- Analyse the main properties of vector fields using the gradient, divergence and curl operators.
- Evaluate path, surface and volume integrals of vector fields.
- Apply the important theorems due to Green, Stokes and Gauss to physical applications.
1 If you need help with your assignment, please contact:
- the academic teaching staff in your unit for guidance in understanding or completing this type of assessment
- the Writing Centre for academic skills support.
2 Indicative time-on-task is an estimate of the time required for completion of the assessment task and is subject to individual variation
Delivery and Resources
Classes
Lectures (beginning in Week 1): There are two one-hour lectures each week.
SGTA classes (beginning in Week 2): There is one two-hour SGTA each week.
The timetable for classes can be found on the University website at: https://publish.mq.edu.au/.
Enrolment can be managed using eStudent at: https://students.mq.edu.au/support/technology/systems/estudent.
Methods of Communication
We will communicate with you via your university email or through announcements on iLearn. Queries to convenors can either be placed on the iLearn discussion board or sent to your lecturers from your university email address.
Policies and Procedures
Macquarie University policies and procedures are accessible from Policy Central (https://policies.mq.edu.au). Students should be aware of the following policies in particular with regard to Learning and Teaching:
- Academic Appeals Policy
- Academic Integrity Policy
- Academic Progression Policy
- Assessment Policy
- Fitness to Practice Procedure
- Assessment Procedure
- Complaints Resolution Procedure for Students and Members of the Public
- Special Consideration Policy
Students seeking more policy resources can visit Student Policies (https://students.mq.edu.au/support/study/policies). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.
To find other policies relating to Teaching and Learning, visit Policy Central (https://policies.mq.edu.au) and use the search tool.
Student Code of Conduct
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/admin/other-resources/student-conduct
Results
Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit connect.mq.edu.au or if you are a Global MBA student contact globalmba.support@mq.edu.au
Academic Integrity
At Macquarie, we believe academic integrity – honesty, respect, trust, responsibility, fairness and courage – is at the core of learning, teaching and research. We recognise that meeting the expectations required to complete your assessments can be challenging. So, we offer you a range of resources and services to help you reach your potential, including free online writing and maths support, academic skills development and wellbeing consultations.
Student Support
Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/
Academic Success
Academic Success provides resources to develop your English language proficiency, academic writing, and communication skills.
- Workshops
- Chat with a WriteWISE peer writing leader
- Access StudyWISE
- Upload an assignment to Studiosity
- Complete the Academic Integrity Module
The Library provides online and face to face support to help you find and use relevant information resources.
Student Services and Support
Macquarie University offers a range of Student Support Services including:
- IT Support
- Accessibility and disability support with study
- Mental health support
- Safety support to respond to bullying, harassment, sexual harassment and sexual assault
- Social support including information about finances, tenancy and legal issues
- Student Advocacy provides independent advice on MQ policies, procedures, and processes
Student Enquiries
Got a question? Ask us via the Service Connect Portal, or contact Service Connect.
IT Help
For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/.
When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.
Changes from Previous Offering
To enable students more time to focus on learning, understanding and reflecting on the content of our unit we have revised the assessment structure as follows. There are now only three assessments: a skills assessment, an assignment and final exam. Although no marks are associated with attendance, all activities provide you with key content designed to help you understand content and complete the assessments.
Unit information based on version 2025.04 of the Handbook