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Unit of study_

MATH1023: Multivariable Calculus and Modelling

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable.


Academic unit Mathematics and Statistics Academic Operations
Unit code MATH1023
Unit name Multivariable Calculus and Modelling
Session, year
Semester 1, 2020
Attendance mode Normal day
Location Camperdown/Darlington, Sydney
Credit points 3

Enrolment rules

MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933
Assumed knowledge

Knowledge of complex numbers and methods of differential and integral calculus including integration by partial fractions and integration by parts as for example in MATH1021 or MATH1921 or MATH1931 or HSC Mathematics Extension 2

Available to study abroad and exchange students


Teaching staff and contact details

Coordinator Daniel Daners,
Lecturer(s) Jesse Thomas Burke ,
Jonathan Spreer,
Administrative staff
Type Description Weight Due Length
Final exam Final exam
written calculations and multiple choice
65% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 1
written calculations
2.5% Week 04
Due date: 19 Mar 2020

Closing date: 29 Mar 2020
10 days
Outcomes assessed: LO1 LO5 LO2
Tutorial quiz Quiz 1 (using the better mark principle)
written calculations
15% Week 07 40 minutes
Outcomes assessed: LO4 LO5
Assignment Assignment 2
written calculations
2.5% Week 10
Due date: 07 May 2020

Closing date: 17 May 2020
10 days
Outcomes assessed: LO1 LO2
Tutorial quiz Quiz 2 (using the better mark principle)
written calculations
15% Week 12 40 minutes
Outcomes assessed: LO6 LO7 LO8 LO9
  • Final exam: There is one examination of 1.5 hours’ duration during the formal examination period at the end of the Semester. Further information about the exam will be made available at a later date on the website.
  • Quizzes: Quizzes will be held during tutorials. You must sit for the quiz during the tutorial in which you are enrolled, unless you have permission from the Student Services Office, issued only for verifiable reasons. Otherwise, your quiz mark may not be recorded. Quizzes will only be returned in the tutorial you sat the quiz and must be collected by week 13. 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.
  • Assignments: There are two assignments, which must be submitted electronically, as PDF files only, in Turnitin (an internet-based plagiarism-prevention service), via the Learning Management System (Canvas) website 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 (check that you can view each page). Late submisions will receive a penalty. 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

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.

Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

Academic integrity

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

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

WK Topic Learning activity Learning outcomes
Week 01 Introduction to models and differential equations Lecture (2 hr) LO3 LO4
Week 02 Separable equations Lecture and tutorial (3 hr) LO5
Week 03 Applications of separable equations Lecture and tutorial (3 hr) LO3 LO5
Week 04 Linear differential equations Lecture and tutorial (3 hr) LO5
Week 05 Second-order differential equations Lecture and tutorial (3 hr) LO6
Week 06 Resonance and coupled differential equations Lecture and tutorial (3 hr) LO6
Week 07 Curves and surfaces in three-dimensional space Lecture and tutorial (3 hr)  
Week 08 Partial derivatives and tangent planes Lecture and tutorial (3 hr) LO7 LO8
Week 09 Second-order partial derivatives and continuity Lecture and tutorial (3 hr) LO7
Week 10 Directional derivatives and the gradient vector Lecture and tutorial (3 hr) LO9
Week 11 Further applications of the partial derivative Lecture and tutorial (3 hr) LO9
Week 12 Optimizing functions of two variables Lecture and tutorial (3 hr) LO10
Week 13 Revision/further applications Lecture and tutorial (3 hr) LO4 LO5 LO6 LO7 LO8 LO9 LO10

Attendance and class requirements

Due to the exceptional circumstances caused by the COVID-19 pandemic, attendance requirements for this unit of study have been amended. Where online tutorials/workshops/virtual laboratories have been scheduled, students should make every effort to attend and participate at the scheduled time. Penalties will not be applied if technical issues, etc. prevent attendance at a specific online class. In that case, students should discuss the problem with the coordinator, and attend another session, if available.

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.

Required readings

  • Course notes: Course Notes for MATH1023 Multivariable Calculus and Modelling. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia, 2020. Available from Kopystop.
  • Reference textbook: James Stewart. Calculus. Cengage Learning. 7th Edition, International Edition, 2012, ISBN 978-0-538-49884-5 or 8th Edition, Metric Version, 2015, ISBN 978-1-305-26672-8. Available from the Co-op Bookshop.

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 rigor 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. calculate partial derivatives and understand their geometric significance
  • LO8. find equations of tangent planes to surfaces
  • LO9. calculate the directional derivative and gradient vector, and understand their physical significance.
  • LO10. optimise functions of two or more variables

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
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.


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