Skip to main content
Unit of study_

MATH1023: Multivariable Calculus and Modelling

Intensive January, 2023 [Block mode] - Camperdown/Darlington, Sydney

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. Students are strongly recommended to complete MATH1021 or MATH1921 Calculus Of One Variable (Advanced) before commencing MATH1023 Multivariable Calculus and Modelling or MATH1923 Multivariable Calculus and Modelling (Adv).

Unit details and rules

Unit code MATH1023
Academic unit Mathematics and Statistics Academic Operations
Credit points 3
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

Coordinator Daniel Hauer,
Lecturer(s) Fernando Viera,
Type Description Weight Due Length
Online task Webwork Online Quizzes
online task (may require calculations)
10% Progressive 3 days for each quiz.
Outcomes assessed: LO1 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 1
Written calculations
5% Week 02
Due date: 22 Jan 2023 at 23:59

Closing date: 29 Jan 2023
7 days
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Assignment Assignment 2
written calculations
10% Week 04
Due date: 05 Feb 2023 at 23:59

Closing date: 12 Feb 2023
7 days
Outcomes assessed: LO1 LO5 LO6 LO7 LO8 LO9 LO10
Online task Quiz
Mulitiple choice
15% Week 05
Due date: 10 Feb 2023 at 16:00
40 minutes
Outcomes assessed: LO1 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Monitored exam
Final exam
Multiple choice and written calculations
60% Week 06
Due date: 15 Feb 2023 at 16:00
1.5 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10

Assessment summary

  • Webwork Online Quizzes: There are ten online quizzes. Each online quiz consists of a set of randomized questions. But only the best 8 out of your 10 quizzes will count, making 10% of your total mark. You cannot apply for special consideration for a single webwork quiz! But the better mark principle will apply for the total 10% - i.e. if your overall exam mark is higher, then your 10% for the Webwork quizzes will come from your exam. The deadline for completion of each quiz is three days later counted from the opening day. The precise schedule for the quizzes is found on Canvas.
  • Quiz: One quiz will be held online through Canvas. The quiz is 40 minutes and will be held in a Zoom session during the regular lecture time. The better mark principle will be used for the quiz, so do not submit an application for Special Consideration or Special Arrangements if you miss the quiz. The better mark principle means that 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. 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. The better mark principle does not apply on assignments!
  • Final Exam: There is one final exam scheduled for this unit of study in week 6. Further information about the exam will be made available at a later date on Canvas.

    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


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

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
Week 01 Introduction to models and differential equations Block teaching (2 hr) LO3 LO4
Separable equations Block teaching (2 hr) LO5
Week 02 Applications of separable equations Block teaching (2 hr) LO3 LO5
Linear differential equations Block teaching (2 hr) LO5
Week 03 Second-order differential equations Block teaching (2 hr) LO6
Resonance and coupled differential equations Block teaching (2 hr) LO6
Week 04 Curves and surfaces in three-dimensional space Block teaching (2 hr)  
Partial derivatives and tangent planes Block teaching (2 hr) LO7 LO8
Further applications of the partial derivative Block teaching (2 hr) LO9
Week 05 Directional derivatives and the gradient vector Block teaching (2 hr) LO9
Second-order partial derivatives and continuity Block teaching (2 hr) LO7
Optimizing functions of two variables Block teaching (2 hr) LO10

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 week) start in Week 2. 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. Since there is no assessment associated with the tutorials do not submit an application for Special Consideration or Special Arrangements for missed tutorials.

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 as PDF on Canvas.
  • 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

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

No changes have been made since this unit was last offered.
  • Lectures: Lectures are online and live. 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.
  • Tutorials: Tutorials start in week 2. 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. If you are absent from a tutorial do not apply for Special Consideration or Special Arrangement, since there is no assessment associated with the missed tutorial.
  • Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1023 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:

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.