Outline

Overview

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.

Unit details and rules

Unit code	MATH1023
Academic unit	Mathematics and Statistics Academic Operations
Credit points	3
Prohibitions ?	MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933
Prerequisites ?	None
Corequisites ?	None
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	Yes

Teaching staff

Coordinator	Daniel Daners, daniel.daners@sydney.edu.au
Lecturer(s)	Haotian Wu, haotian.wu@sydney.edu.au
	Leo Tzou, leo.tzou@sydney.edu.au
	Jesse Burke, jesse.burke@sydney.edu.au

Type	Description	Weight	Due	Length
Final exam (Open book)	Final exam multiple choice and written calculations	65%	Formal exam period	1.5 hours
Outcomes assessed:
Assignment	Assignment 1 written calculations	4%	Week 03 Due date: 07 Sep 2020 at 23:59 Closing date: 17 Sep 2020	10 days
Outcomes assessed:
Online task	Quiz written calculations	15%	Week 07 Due date: 13 Oct 2020 at 23:59 Closing date: 13 Oct 2020	40 minutes
Outcomes assessed:
Assignment	Assignment 2 written calculations	8%	Week 10 Due date: 02 Nov 2020 at 23:59 Closing date: 12 Nov 2020	10 days
Outcomes assessed:
Assignment	Webwork Online Quizzes online task (may require calculations)	8%	Weekly	Weeks 2-6, 8-12
Outcomes assessed:
= Type C final exam ?

Assessment summary

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 submisions will receive a penalty.
Quiz: One quiz will be held online through Canvas. The quiz is 40 Minutes and has 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 quiz so do not submit an application for Special Consideration or Special Arrangements if you miss a 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.
Webwork Online Quizzes: There are ten weekly online quizzes. Each online quiz consists of a set of randomized questions. The best 8 of your 10 quizzes will count, making each worth 1%. You cannot apply for special consideration for the quizzes. The better mark principle will apply for the total 8% - i.e. if your overall exam mark is higher, then your 8% for the Webwork quizzes will come from your exam. The deadline for completion of each quiz is 23:59 on Wednesday (starting in week 2). The precise schedule for the quizzes is found on Canvas.
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.

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	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 sydney.edu.au/students/guide-to-grades.

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.

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.

Weekly schedule

WK	Topic	Learning activity
Week 01	Introduction to models and differential equations	Lecture (2 hr)
Week 02	Separable equations	Lecture and tutorial (3 hr)
Week 03	Applications of separable equations	Lecture and tutorial (3 hr)
Week 04	Linear differential equations	Lecture and tutorial (3 hr)
Week 05	Second-order differential equations	Lecture and tutorial (3 hr)
Week 06	Resonance and coupled differential equations	Lecture and tutorial (3 hr)
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)
Week 09	Second-order partial derivatives and continuity	Lecture and tutorial (3 hr)
Week 10	Directional derivatives and the gradient vector	Lecture and tutorial (3 hr)
Week 11	Further applications of the partial derivative	Lecture and tutorial (3 hr)
Week 12	Optimizing functions of two variables	Lecture and tutorial (3 hr)

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.

Attendance: Students are expected to attend a minimum of 80% of timetabled activities for a unit of study, 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: 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

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. 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
Learning outcomes

Responding to student feedback

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

No changes have been made since this unit was last offered.

Additional information

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

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.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

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

Media

Student links

About us

Connect

Current students

MATH1023: Multivariable Calculus and Modelling

Semester 2, 2020 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

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

Media

Student links

About us

Connect