Unit of study_

# MATH1023: Multivariable Calculus and Modelling

## 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. Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

### Details

Academic unit Mathematics and Statistics Academic Operations MATH1023 Multivariable Calculus and Modelling Semester 1, 2021 Normal day Remote 3

### Enrolment rules

 Prohibitions ? MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 None None 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 Yes

### Teaching staff and contact details

Coordinator Jonathan Spreer, jonathan.spreer@sydney.edu.au MATH1023@sydney.edu.au Please send all email regarding MATH1023 to this address. It goes to the unit of study coordinator, the lecturers and administrative support.

## Assessment

Type Description Weight Due Length
Final exam (Record+) 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: 17 Mar 2021

Closing date: 27 Mar 2021
10 days
Outcomes assessed:
written calculations
15% Week 07
Due date: 21 Apr 2021

Closing date: 21 Apr 2021
40 minutes
Outcomes assessed:
Assignment Assignment 2
written calculations
8% Week 10
Due date: 12 May 2021

Closing date: 22 May 2021
10 days
Outcomes assessed:
Assignment Webwork Online Quizzes
8% Weekly Weeks 2-6, 8-13
Outcomes assessed:
= Type B final exam

• 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. A mark of zero will be awarded for all submissions more than 10 days past the original due date. Further extensions past this time will not be permitted.
• Quiz: One quiz will be held online through Canvas. The quiz is 40 minutes. 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.
• 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.

### 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.

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.

## Weekly schedule

WK Topic Learning activity Learning outcomes
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)
Week 13 Revision/further applications 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 on-campus or online tutorials/workshops/laboratories have been scheduled, students should make every effort to attend and participate at the scheduled time. If you are unable to attend for any reason (e.g. health or technical issues) you should and attend another session, if available. Penalties will not apply if you cannot attend your scheduled class.

• 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.

• 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.

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

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

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Closing the loop

The number of teaching weeks has been set back to 13.

### 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.