Students

MATH2020 – Vector Calculus and Complex Analysis

2021 – Session 2, Special circumstances

Session 2 Learning and Teaching Update

The decision has been made to conduct study online for the remainder of Session 2 for all units WITHOUT mandatory on-campus learning activities. Exams for Session 2 will also be online where possible to do so.

This is due to the extension of the lockdown orders and to provide certainty around arrangements for the remainder of Session 2. We hope to return to campus beyond Session 2 as soon as it is safe and appropriate to do so.

Some classes/teaching activities cannot be moved online and must be taught on campus. You should already know if you are in one of these classes/teaching activities and your unit convenor will provide you with more information via iLearn. If you want to confirm, see the list of units with mandatory on-campus classes/teaching activities.

Visit the MQ COVID-19 information page for more detail.

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor/Lecturer
Paul Bryan
Contact via Email
Please refer to iLearn
Lecturer
Ross Moore
Contact via Email
Please refer to iLearn
Ross Moore
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://students.mq.edu.au/important-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

HURDLES: This unit has no hurdle requirements.

ASSIGNMENT SUBMISSION:  Assignment submission will be online through the iLearn page.

Submit assignments online via the appropriate assignment link on the iLearn page. A personalised cover sheet is not required with online submissions. Read the submission statement carefully before accepting it as there are substantial penalties for making a false declaration.

•   Assignment submission is via iLearn. You should upload this as a single scanned PDF file.

•   Please note the quick guide on how to upload your assignments provided on the iLearn page.

•   Please make sure that each page in your uploaded assignment corresponds to only one A4 page (do not upload an A3 page worth of content as an A4 page in landscape). If you are using an app like Clear Scanner, please make sure that the photos you are using are clear and shadow-free.

•   It is your responsibility to make sure your assignment submission is legible.

•   If there are technical obstructions to your submitting online, please email us to let us know.

You may submit as often as required prior to the due date/time. Please note that each submission will completely replace any previous submissions. It is in your interests to make frequent submissions of your partially completed work as insurance against technical or other problems near the submission deadline.

LATE SUBMISSION:  All assignments must be submitted by the official due date and time. No marks will be given to late work unless an extension has been granted following a successful application for Special Consideration. Please contact the unit convenor for advice as soon as you become aware that you may have difficulty meeting any of the assignment deadlines. It is in your interests to make frequent submissions of your partially completed work. Note that later submissions completely replace any earlier submission, and so only the final submission made before the due date will be marked.

FINAL EXAM POLICY:  You are advised that it is Macquarie University policy not to set early examinations for individuals or groups of students. All students are expected to ensure that they are available until the end of the teaching semester, that is, the final day of the official examination period. The only excuse for not sitting an examination at the designated time is because of documented illness or unavoidable disruption. In these special circumstances, you may apply for special consideration via ask.mq.edu.au.

SUPPLEMENTARY EXAMINATIONS: 

IMPORTANT: If you receive special consideration for the final exam, a supplementary exam will be scheduled in the interval between the regular exam period and the start of the next session. If you apply for special consideration, you must give the supplementary examination priority over any other pre-existing commitments, as such commitments will not usually be considered an acceptable basis for a second application for special consideration. Please ensure you are familiar with the policy prior to submitting an application. You can check the supplementary exam information page on FSE101 in iLearn (https://bit.ly/FSESupp) for dates, and approved applicants will receive an individual notification sometime in the week prior to the exam with the exact date and time of their supplementary examination.

Assessment Tasks

Name Weighting Hurdle Due
Test 1 (Online) 15% No Week 4
Assignment 1 10% No Week 6
Test 2 (Online) 15% No Week 10
Assignment 2 10% No Week 12
Final exam 50% No Exam period

Test 1 (Online)

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

Online 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 6
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 (Online)

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

 

Online 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.

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.

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 Learning Skills Unit 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: there 2 x 1hr lectures and a 1hr SGTA each week.

Required and Recommended Texts and/or Materials

Lecture notes will be available on iLearn.

The following texts provide useful references for various sections of the course:

  • Churchill and Brown; Complex variables and applications, (McGraw–Hill)  library call number QA331 .C524
  • Marsden and Tromba; Vector Calculus, (Wiley)  library call number QA303 .M338

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Students seeking more policy resources can visit the Student Policy Gateway (https://students.mq.edu.au/support/study/student-policy-gateway). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

If you would like to see all the policies relevant to Learning and Teaching visit Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central).

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

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

Learning Skills

Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to help you improve your marks and take control of your study.

The Library provides online and face to face support to help you find and use relevant information resources. 

Student Enquiry Service

For all student enquiries, visit Student Connect at ask.mq.edu.au

If you are a Global MBA student contact globalmba.support@mq.edu.au

Equity Support

Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.

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.