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.

### Unit details and rules

Unit code MATH1023 Mathematics and Statistics Academic Operations 3 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

Coordinator Daniel Daners, daniel.daners@sydney.edu.au Jesse Burke Jonathan Spreer

## Assessment

Type Description Weight Due Length
Final exam Final exam
written calculations and multiple choice
65% Formal exam period 1.5 hours
Outcomes assessed:
Assignment Assignment 1
written calculations
2.5% Week 04
Due date: 19 Mar 2020 at 23:59

Closing date: 29 Mar 2020
10 days
Outcomes assessed:
Tutorial quiz Quiz 1 (using the better mark principle)
written calculations
15% Week 07 40 minutes
Outcomes assessed:
Assignment Assignment 2
written calculations
2.5% Week 10
Due date: 07 May 2020 at 23:59

Closing date: 17 May 2020
10 days
Outcomes assessed:
Tutorial quiz Quiz 2 (using the better mark principle)
written calculations
15% Week 12 40 minutes
Outcomes assessed:

### Assessment summary

• 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

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.

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 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 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.

• 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

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

## 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.