Students

MATH2020 – Vector Calculus and Complex Analysis

2023 – Session 2, In person-scheduled-weekday, North Ryde

General Information

Download as PDF
Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor
Paul Bryan
paul.bryan@mq.edu.au
Contact via Via email
12WW 706
Unit Convenor
Frank Valckenborgh
frank.valckenborgh@mq.edu.au
Contact via Via email
12WW 613
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

Requirements to Pass This Unit

To pass this unit, you must achieve a total mark equal to or greater than 50%.

 

Late Assessment Submission Penalty

Unless a Special Consideration request has been submitted and approved, a 5% penalty (of the total possible mark of the task) will be applied for each day a written report or presentation 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. 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 timesensitive tasks, such as scheduled tests/exams, performance assessments/presentations, and/or scheduled practical assessments/labs, please apply for Special Consideration.

Assessments where Late Submissions will be accepted

  • Tests - NO, unless Special Consideration is Granted
  • Assignments - YES, Standard Late Penalty applies

 

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 ask.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 con- venor and submit a Special Consideration request through ask.mq.edu.au.

Assessment Tasks

Name Weighting Hurdle Due
Final exam 50% No Exam period
Test 1 15% No Week 4
Assignment 1 10% No Week 7
Test 2 15% No Week 10
Assignment 2 10% No Week 12

Final exam

Assessment Type 1: Examination
Indicative Time on Task 2: 15 hours
Due: Exam period
Weighting: 50%

Summative examination, held during the university examination period.
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.

Test 1

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 10 hours
Due: Week 4
Weighting: 15%

 

Test

 
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 1

Assessment Type 1: Problem set
Indicative Time on Task 2: 10 hours
Due: Week 7
Weighting: 10%

The assignments reinforce and build on material from lectures, and involve calculations and explanations.
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.

Test 2

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

 

Test

 
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 2

Assessment Type 1: Problem set
Indicative Time on Task 2: 10 hours
Due: Week 12
Weighting: 10%

The assignments reinforce and build on material from lectures, and involve calculations and explanations.
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): Students must register in and should attend one two-hour class per week.

 

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.

 

COVID Information

For the latest information on the University’s response to COVID-19, please refer to the Coronavirus infection page on the Macquarie website: https://www.mq.edu.au/about/coronavirus-faqs. Remember to check this page regularly in case the information and requirements change during semester. If there are any changes to this unit in relation to COVID, these will be communicated via iLearn.

Unit Schedule

Vector Calculus

Week Topic Assessment
1 Differentiation, curves, vector fields  
2 Line integrals  
3 Green's theorem, Surfaces  
4 Surface integrals,flux Test 1
5 Divergence Theorem, Kelvin-Stokes' Theorem  
6 Review and catch up  

 

Complex Analysis

Week Topic Assessment
7 Introduction to Complex Analysis,  Complex Functions Assignment 1
8 Analytic Functions,  Complex Logarithm  
9 Complex Integration  
10 Cauchy's Integral Theorem,   Cauchy's Integral Formula Test 2
11 Taylor's Theorem,   Laurent Series  
12 Isolated Zeros,  Isolated Singularities Assignment 2
13  Cauchy's Residue Theorem                      Review  

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:

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 ask.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/

The Writing Centre

The Writing Centre provides resources to develop your English language proficiency, academic writing, and communication skills.

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:

Student Enquiries

Got a question? Ask us via AskMQ, 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

We value student feedback to be able to continually improve the way we offer our units. As such we encourage students to provide constructive feedback via student surveys, to the teaching staff directly, or via the FSE Student Experience & Feedback link in the iLearn page. Student feedback from the previous offering of this unit was positive overall, with students pleased with the clarity around assessment requirements and the level of support from teaching staff. As such, no change to the delivery of the unit is planned, however we will continue to strive to improve the level of support and the level of student engagement.

Unit information based on version 2023.02 of the Handbook