Outline

Overview

This unit starts with an investigation of linearity: linear functions, general principles relating to the solution sets of homogeneous and inhomogeneous linear equations (including differential equations), linear independence and the dimension of a linear space. The study of eigenvalues and eigenvectors, begun in junior level linear algebra, is extended and developed. The unit then moves on to topics from vector calculus, including vector-valued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; path-independent integrals and conservative fields; flux across a curve), iterated integrals (double and triple integrals; polar, cylindrical and spherical coordinates; areas, volumes and mass; Green's Theorem), flux integrals (flow through a surface; flux integrals through a surface defined by a function of two variables, though cylinders, spheres and parametrised surfaces), Gauss' Divergence Theorem and Stokes' Theorem.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	{(MATH1X61 or MATH1971) or [(MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (MATH1014 or MATH1X02)]} and (MATH1X62 or MATH1972 or MATH1013 or MATH1X23 or MATH1X03 or MATH1933 or MATH1907)
Corequisites ?	None
Prohibitions ?	MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922
Assumed knowledge ?	None
Available to study abroad and exchange students	No

Teaching staff

Coordinator	Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au
Lecturer(s)	Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au
Lecturer(s)	Ruibin Zhang, ruibin.zhang@sydney.edu.au

Assessment

The census date for this unit availability is 23 January 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam	Final exam Multiple choice and written calculations	56%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Out-of-class quiz	Online quizzes Online quizzes	8%	Multiple weeks	45 minutes per quiz	AI allowed
Outcomes assessed:
Out-of-class quiz	Early feedback task #earlyfeedbacktask	2%	Week 01 Due date: 18 Jan 2026 at 23:59 Closing date: 18 Jan 2026	45 minutes	AI allowed
Outcomes assessed:
Written work	Assignment 1 written calculations	7%	Week 02 Due date: 22 Jan 2026 at 23:59 Closing date: 29 Jan 2026	3-5 pages	AI allowed
Outcomes assessed:
In-person written or creative task	Mid-semester test Multiple choice or written answers	18%	Week 03 Due date: 30 Jan 2026 at 15:00	40 minutes	AI prohibited
Outcomes assessed:
Written work	Assignment 2 written calculations	7%	Week 04 Due date: 05 Feb 2026 at 23:59 Closing date: 12 Feb 2026	3-5 pages	AI allowed
Outcomes assessed:
Contribution	Tutorials Contribution to tutorials	2%	Weekly	50 minutes per class	AI allowed
Outcomes assessed:
= early feedback task ?

Early feedback task

This unit includes an early feedback task, designed to give you feedback prior to the census date for this unit. Details are provided in the Canvas site and your result will be recorded in your Marks page. It is important that you actively engage with this task so that the University can support you to be successful in this unit.

Assessment summary

Assignments: There are two short release assignments. Each must be submitted electronically, as one single typeset or scanned PDF file only, via Canvas by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly and that it is complete (check that you can view each page). Late submissions will receive a penalty. A mark of zero will be awarded for all submissions more than 7 days past the original due date. Further extensions past this time will not be permitted. The maximum extension you can be awarded through Special Consideration for the assignments is 7 calendar days. If you are affected for more than 7 calendar days you will be granted a mark adjustment. This means that your final exam mark will count instead for the assignment mark. The closing date for submissions (with a late penalty) is the same for all students. It is not changed if you are granted an extension. This allows for timely release of the marks and feedback. Note that the assignments are not eligible for a Simple Extension through the Special Consideration system since they are short release assignments (released to you to complete within 10 working days).
Quiz: One quiz will be held in-person on campus during Week 3. You must sit the quiz at the time and location that appears as Assessment on your timetable. If you are unable to sit the quiz at that time for a valid reason, then you have the option to apply for Special Consideration or Special Arrangements. Quiz feedback will be returned through Canvas.
Online Quizzes: There are six online quizzes (through Canvas and equally weighted) and the marks for the best five count. The first one is used for the Early Feedback Task. Each online quiz consists of a set of randomized questions. If you choose to apply for special consideration for the online quizzes, and your application is approved, then you will be granted a mark adjustment - i.e. your 10% for the online quizzes will come from your final exam. The deadline for completion of each quiz is 23:59 Sunday (starting in week 1). The precise schedule for the quizzes is found on Canvas. We recommend that you follow the due dates outlined above to gain the most benefit from these quizzes.
Tutorial Contribution: This is a satisfactory/non-satisfactory mark assessing whether or not you contribute to class activities during the tutorials starting in Week 1. It is 0.25 marks per tutorial class up to 8 tutorials (there are 11 tutorials).
Final Exam: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. Further information about the exam will be made available at a later date on Canvas. If a second replacement exam is required, this exam may be delivered via an alternative secured assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative secured assessment will be determined by the unit coordinator.

Detailed information for each assessment can be found on Canvas.

Even though the use of AI is allowed for some assessments, it is better for your learning to do your own work to complete your assessments.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name	Mark range	Description
High distinction	85 - 100	Representing complete or close to complete mastery of the material.
Distinction	75 - 84	Representing excellence, but substantially less than complete mastery.
Credit	65 - 74	Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
Pass	50 - 64	Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.
Fail	0 - 49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the Academic Integrity Policy.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the Academic Honesty Education Module (AHEM) which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Week 01	Linear systems, Gaussian elimination, vector spaces and subspaces, linear combinations; vector equations of lines and curves (revision), arc length, vector fields, two types of line integrals, work done by a force, grad and curl, normals to surfaces	Lecture (12 hr)
Week 01	Linear systems, Gaussian elimination, vector spaces and subspaces; vector equations of lines and curves (revision), arc length, vector fields, two types of line integrals, work done by a force	Tutorial (2 hr)
Week 02	Span, linear dependence and independence, basis and dimension; conservative fields and potential functions, double integrals, polar coordinates, Green's theorem	Lecture (12 hr)
Week 02	Subspaces, linear combinations, span, linear dependence and independence, basis; grad and curl, normals to surfaces, conservative fields and potential functions	Tutorial (3 hr)
Week 03	Basis and dimension, Lagrange interpolation, column space, null space, rank, nullity and linear transformations; Green's theorem continued, flux across a curve, surface area, surface integrals, flux across a surface, cylindrical and spherical coordinates	Lecture (8 hr)
Week 03	Basis and dimension, Lagrange interpolation, column space, null space, rank, nullity, linear transformations; double integrals, polar coordinates, Green's theorem	Tutorial (2 hr)
Week 04	Eigenvalues and eigenvectors, diagonalisation theorem, linear recurrence relations, Leslie population model; triple integrals, volume and mass revisited, cylindrical and spherical coordinates, Gauss' divergence theorem	Lecture (12 hr)
Week 04	Eigenvalues and eigenvectors, diagonalisation theorem, linear recurrence relations; Green's theorem continued, flux across a curve, surface area, surface integrals, flux across a surface, cylindrical and spherical coordinates, triple integrals, volume and mass revisited	Tutorial (3 hr)
Week 05	Systems of linear differential equations, linear mathematics revision; Stokes' theorem, vector calculus revision	Lecture (8 hr)
Week 05	Linear recurrence relations, Leslie population model, systems of linear differential equations; cylindrical and spherical coordinates, Gauss' divergence theorem, Stokes' theorem	Tutorial (2 hr)

Attendance and class requirements

Lecture attendance: You are expected to attend lectures. If you do not attend lectures you should at least follow the lecture recordings available through Canvas.
Tutorial attendance: Tutorials (one per day) start on Day 2. You should attend the tutorial given on your personal timetable. Attendance at tutorials and contribution will be recorded to determine the contribution mark. Your attendance will not be recorded unless you attend the tutorial in which you are enrolled. We strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions.

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

See the Canvas site for reference material.

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. solve a system of linear equations
LO2. apply the subspace test in several different vector spaces
LO3. calculate the span of a given set of vectors in various vector spaces
LO4. test sets of vectors for linear independence and dependence
LO5. find bases of vector spaces and subspaces
LO6. find a polynomial of minimum degree that fits a set of points exactly
LO7. find bases of the fundamental subspaces of a matrix
LO8. test whether an n × n matrix is diagonalisable, and if it is find its diagonal form
LO9. apply diagonalisation to solve recurrence relations and systems of DEs
LO10. extended (from first year) their knowledge of vectors in two and three dimensions, and of functions of several variables
LO11. evaluate certain line integrals, double integrals, surface integrals and triple integrals
LO12. understand the physical and geometrical significance of these integrals
LO13. know how to use the important theorems of Green, Gauss and Stokes.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

The peer learning task has been removed and the other assessments have reweighted.

Additional information

Lectures: Lectures are face-to-face and streamed live with online access from Canvas.
Tutorials: Tutorials are small classes in which you are expected to work through questions from the tutorial sheet in small groups on the white board. The role of the tutor is to provide support and to some extent give feedback on your solutions written on the board.

Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH2061 Canvas page. Solutions to tutorial exercises for week n will usually be posted on the web by the afternoon of the Friday of week n.
Ed Discussion forum: https://edstem.org

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

Disclaimer

Important: the University of Sydney regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

MATH2061: Linear Mathematics and Vector Calculus

Intensive January, 2026 [Block mode] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links