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Unit outline_

MATH1933: Multivariable Calculus and Modelling (SSP)

Semester 2, 2023 [Normal day] - Camperdown/Darlington, Sydney

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1923 Multivariable Calculus and Modelling (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 3
MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923
Assumed knowledge

(HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent

Available to study abroad and exchange students


Teaching staff

Coordinator Daniel Daners,
Type Description Weight Due Length
Supervised exam
Final exam
multiple choice and written calculations
60% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO14
Assignment Assignment 1
written calculations
3% Week 03
Due date: 17 Aug 2023 at 23:59

Closing date: 27 Aug 2023
3-5 pages (as a guide)
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Assignment Special Assignment 1
written calculations
3% Week 05
Due date: 31 Aug 2023 at 23:59

Closing date: 10 Sep 2023
2-4 pages (as a guide)
Outcomes assessed: LO1 LO13 LO14
Online task Quiz 1
multiple choice or written answers
8.5% Week 06
Due date: 07 Sep 2023 at 23:59

Closing date: 07 Sep 2023
40 minutes
Outcomes assessed: LO3 LO6 LO5 LO4
Assignment Assignment 2
Written calculations
6% Week 08
Due date: 21 Sep 2023 at 23:59

Closing date: 01 Oct 2023
6-8 pages (as a guide)
Outcomes assessed: LO1 LO9 LO8 LO7 LO6 LO2
Assignment Special Assignment 2
written calculations
3% Week 09
Due date: 05 Oct 2023 at 23:59

Closing date: 15 Oct 2023
2-4 pages (as a guide)
Outcomes assessed: LO1 LO13 LO14
Online task Quiz 2
multiple choice or written answers
8.5% Week 11
Due date: 19 Oct 2023 at 23:59

Closing date: 19 Oct 2023
40 minutes
Outcomes assessed: LO7 LO10 LO9 LO8
Assignment Special Assignment 3
written calculations
3% Week 13
Due date: 02 Nov 2023 at 23:59

Closing date: 12 Nov 2023
2-4 pages (as a guide)
Outcomes assessed: LO1 LO13 LO14
Participation Seminar participation
Participation in class discussion
5% Weekly Weekly
Outcomes assessed: LO13

Assessment summary

  • Quizzes: Two quizzes will be held online through Canvas. The quizzes are 40 minutes and have to be submitted by the closing time of 23:59 on the due date. The quiz can be taken any time during the 24 hour period before the closing time. The better mark principle will be used for the quizzes so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that for each quiz, the quiz counts if and only if it is better than or equal to your exam mark. If your quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead.
  • Special assignments: The better mark principle with apply for the Special Assignment component (9%) if all Special Assignments are submitted with a substantial attempt.
  • Seminar participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class and group discussions during the seminars. It is 0.5 marks per seminar session up to 10 sessions (there are 12 sessions).
  • Final Exam: There is one examination during the examination period at the end of Semester. 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 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 can be found 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


High distinction

85 - 100

Representing complete or close to complete mastery of the material.


75 - 84

Representing excellence, but substantially less than complete mastery.


65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.


50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.


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.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

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.

WK Topic Learning activity Learning outcomes
Multiple weeks Special Topics Seminar (12 hr) LO13 LO14
Week 01 Introduction to models Lecture (2 hr) LO3
Week 02 First-order differential equations Lecture and tutorial (3 hr) LO4 LO5
Week 03 Integrating factors and direction fields Lecture and tutorial (3 hr) LO4 LO5
Week 04 Second-order differential equations. Boundary conditions Lecture and tutorial (3 hr) LO6
Week 05 Systems of linear differential equations and interpretation through diagonalisation. Introduction to phase plane analysis Lecture and tutorial (3 hr) LO6
Week 06 Functions of more than one real variable Lecture and tutorial (3 hr) LO7
Week 07 Limits of functions of more than one real variable Lecture and tutorial (3 hr) LO7
Week 08 Partial derivatives. Tangent planes. Linear approximation Lecture and tutorial (3 hr) LO8 LO9
Week 09 Directional derivatives. Gradient vector and applications Lecture and tutorial (3 hr) LO10
Week 10 Chain rule. Implicit differentiation Lecture and tutorial (3 hr) LO10
Week 11 Optimising functions of two or more variables Lecture and tutorial (3 hr) LO11
Week 12 Further optimisation and interpretation using diagonalisation Lecture and tutorial (3 hr) LO12
Week 13 Revision Lecture and tutorial (3 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14

Attendance and class requirements

  • Attendance: Students are expected to attend a minimum of 80% of timetabled activities for this unit, unless granted exemption by the Associate Dean. For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%.
  • Tutorial attendance: You should attend the tutorial given on your personal timetable. Attendance at tutorials will be recorded. Your attendance will not be recorded unless you attend the tutorial in which you are enrolled. While there is no penalty if 80% attendance is not met 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 3 credit point unit, this equates to roughly 60-75 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. apply mathematical logic and rigour to solving problems
  • LO2. express mathematical ideas and arguments coherently in written form
  • LO3. set up differential equations which arise from mathematical models of interest to scientists and engineers
  • LO4. understand the relationship between a first-order differential equation, its direction field, and its solution curves
  • LO5. solve separable and first-order linear differential equations
  • LO6. solve second-order homogeneous linear differential equations with constant coefficients
  • LO7. understand the concepts of limit and derivative for functions of more than one variable
  • LO8. calculate partial derivatives and understand their geometric significance
  • LO9. find equations of tangent planes to surfaces
  • LO10. calculate the direction derivative and gradient vector, and understand their physical significance
  • LO11. optimise functions of two or more variables
  • LO12. understand the connections between multivariable calculus and linear algebra
  • LO13. gain an appreciation of a diverse range of mathematical problems and applications through participating in class discussions and the completion of assignments
  • LO14. grasp new mathematical concepts beyond routine methods and calculations.

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

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

No changes have been made 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.


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.