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Unit outline_

MATH2061: Linear Mathematics and Vector Calculus

Intensive January, 2025 [Block mode] - Camperdown/Darlington, Sydney

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
Ruibin Zhang, ruibin.zhang@sydney.edu.au
The census date for this unit availability is 24 January 2025
Type Description Weight Due Length
Supervised exam
? 
Final Exam
Multiple choice and written calculations
60% February exam weeks 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14
Participation Tutorials
Participation in tutorials
4% Progressive 50 minutes per teaching day
Outcomes assessed: LO1 LO14 LO13 LO12 LO11 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Small test Early Online Quiz
#earlyfeedbacktask
2% Week 01
Due date: 19 Jan 2025 at 23:59

Closing date: 19 Jan 2025
40 minutes
Outcomes assessed: LO1 LO11 LO10 LO3 LO2
Assignment Assignment 1
written calculations
5% Week 02
Due date: 23 Jan 2025 at 23:59

Closing date: 30 Jan 2025
3-5 pages
Outcomes assessed: LO1 LO2 LO3 LO4 LO10 LO11 LO12 LO13 LO14
Tutorial quiz Quiz 1
Multiple choice or written answers
12% Week 03
Due date: 30 Jan 2025 at 16:00

Closing date: 30 Jan 2025
40 minutes
Outcomes assessed: LO1 LO14 LO13 LO12 LO11 LO10 LO5 LO4 LO3 LO2
Assignment Assignment 2
written calculations
5% Week 04
Due date: 04 Feb 2025 at 23:59

Closing date: 11 Feb 2025
3-5 pages
Outcomes assessed: LO10 LO11 LO12 LO13 LO5 LO6 LO7 LO8 LO9 LO14
Tutorial quiz Quiz 2
Multiple choice or written answers
12% Week 05
Due date: 12 Feb 2025 at 16:00

Closing date: 12 Feb 2025
40 minutes
Outcomes assessed: LO10 LO8 LO7 LO6 LO5 LO14 LO13 LO12 LO11

Assessment summary

  • Quizzes: Two quizzes will be held on campus. Each quiz is 40 minutes and has to be submitted during your timetabled computer lab on the due date. Detailed information for each quiz will be available on Canvas. Please submit an application for Special Consideration or Special Arrangements if you miss a quiz.
  • Assignments: There are two assignments. Each assignment must be submitted electronically, as one single typeset or scanned PDF file only via the 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 penalties according to the University policy. Detailed information for each assignment will be available on Canvas.
  • Tutorial Participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class activities during the tutorials. It is 0.5 marks per tutorial class up to 8 tutorials (there are 12 tutorials).
  • Final Exam:  There is one supervised final exam to this unit of study held in the exam period. Further information about the exam will be made available on Canvas before the exam. If a second replacement exam is required, this exam may be delivered via an alternative 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 assessment will be determined by the unit coordinator. 

Detailed information for each assessment will be available on Canvas.

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.

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 Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

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 2023 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 2023. 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

WK Topic Learning activity Learning outcomes
Week 01 Linear systems, Gaussian elimination, vector spaces and subspaces; vector equations of lines and curves (revision), arc length, two types of line integrals and work done by a force Lecture (4 hr) LO1 LO2 LO10
Linear systems, Gaussian elimination, vector spaces and subspaces; vector equations of lines and curves (revision), arc length, two types of line integrals and work done by a force Lecture and tutorial (5 hr) LO1 LO2 LO10
Subspaces, linear combinations, span, linear dependence and independence; vector fields, grad and curl, normals to surfaces, conservative fields and potential functions Lecture and tutorial (5 hr) LO2 LO3 LO4 LO5 LO10 LO11 LO12
Week 02 Subspaces, linear combinations, span, linear dependence and independence; vector fields, grad and curl, normals to surfaces, conservative fields and potential functions Lecture and tutorial (5 hr) LO2 LO3 LO4 LO5 LO10 LO11 LO12
Linear dependence and independence, span, basis and dimension; double integrals, area, volume, mass, divergence of a vector field, Green's theorem and flux across a curve. Lecture and tutorial (5 hr) LO3 LO4 LO5 LO11 LO12 LO13 LO14
Linear dependence and independence, span, basis and dimension; double integrals, area, volume, mass, divergence of a vector field, Green's theorem and flux across a curve. Lecture and tutorial (5 hr) LO3 LO4 LO5 LO11 LO12 LO13 LO14
Week 03 Basis and dimension, Lagrange interpolation, column space, null space, rank, nullity and linear transformations; Green's theorem continued, surface area, surface integrals, flux across a surface, polar, cylindrical and spherical coordinates Lecture and tutorial (5 hr) LO5 LO6 LO7 LO11 LO12 LO13 LO14
Basis and dimension, Lagrange interpolation, column space, null space, rank, nullity and linear transformations; Green's theorem continued, surface area, surface integrals, flux across a surface, polar, cylindrical and spherical coordinates Lecture and tutorial (5 hr) LO5 LO6 LO7 LO11 LO12 LO13 LO14
Week 04 Eigenvalues and eigenvectors, diagonalisation theorem and Leslie population model; triple integrals, volume and mass revisited and Gauss' divergence theorem Lecture and tutorial (5 hr) LO8 LO9 LO11 LO12 LO13 LO14
Eigenvalues and eigenvectors, diagonalisation theorem and Leslie population model; triple integrals, volume and mass revisited and Gauss' divergence theorem Lecture and tutorial (5 hr) LO8 LO9 LO11 LO12 LO13 LO14
Recurrence relations and systems of linear differential equations; triple integrals in cylindrical/spherical coordinates, Stokes' theorem and connections between different types of integrals Lecture and tutorial (5 hr) LO9 LO11 LO12 LO13 LO14
Week 05 Recurrence relations and systems of linear differential equations; triple integrals in cylindrical/spherical coordinates, Stokes' theorem and connections between different types of integrals Lecture and tutorial (5 hr) LO9 LO11 LO12 LO13 LO14
Revision Lecture and tutorial (5 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14

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.

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.

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. evaluate certain line integrals, double integrals, surface integrals and triple integrals
  • LO13. understand the physical and geometrical significance of these integrals
  • LO14. 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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

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

Information on assessments has been updated since this unit was last offered.

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.

General Laboratory Safety Rules

  • No eating or drinking is allowed in any laboratory under any circumstances
  • A laboratory coat and closed-toe shoes are mandatory
  • Follow safety instructions in your manual and posted in laboratories
  • In case of fire, follow instructions posted outside the laboratory door
  • First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
  • As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

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