Outline

Overview

This is the advanced version of MATH2021, with more emphasis on the underlying concepts and mathematical rigour. The vector calculus component of the course includes: parametrised curves and surfaces, vector fields, div, grad and curl, gradient fields and potential functions, Lagrange Multiplier Method, line integrals of different types (arc length, work, etc.), conservative fields, double and triple integrals, change of variable formulas, polar, cylindrical and spherical coordinates, areas, volumes and mass, flux integrals, and Green's Gauss' and Stokes' Theorems. The Differential Equations component of the course focuses on ordinary and partial differential equations (ODEs and PDEs) with applications with more complexity and depth. It provides a more thorough grounding in these techniques to enable students to build on the concepts in their subsequent courses. The main topics are: first and second order ODEs (including inhomogeneous equations), series solutions near a regular point, higher order ODEs and systems of first order equations, matrix equations, various methods (variation of parameters, undetermined coefficients, reduction of order), an introduction to PDEs, and first methods of solutions (including separation of variables, and Fourier Series). It could extend to the Laplace and Fourier Transform and elementary Sturm-Liouville Theory.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	[(MATH1921 or MATH1931 or MATH1901 or MATH1906) or (a mark of 65 or above in MATH1021 or MATH1001)] and [MATH1902 or (a mark of 65 or above in MATH1002)] and [(MATH1923 or MATH1933 or MATH1903 or MATH1907) or (a mark of 65 or above in MATH1023 or MATH1003)]
Corequisites ?	None
Prohibitions ?	MATH2021 or MATH2065 or MATH2965 or (MATH2061 and MATH2022) or (MATH2061 and MATH2922) or (MATH2961 and MATH2022) or (MATH2961 and MATH2922) or MATH2067
Assumed knowledge ?	None
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Zhou Zhang, zhou.zhang@sydney.edu.au
Lecturer(s)	Zhou Zhang, zhou.zhang@sydney.edu.au

Type	Description	Weight	Due	Length
Supervised exam ?	Final Exam Supervised exam	60%	Formal exam period	2 hours
Outcomes assessed:
Assignment	Assignment Written assignment task	10%	Week 05 Due date: 26 Mar 2023 at 23:59	2 weeks
Outcomes assessed:
Small test	Quiz 1 Quiz in Practice Class	15%	Week 07 Due date: 06 Apr 2023 at 15:00	1 hour
Outcomes assessed:
Small test	Quiz 2 Quiz in Practice Class	15%	Week 11 Due date: 11 May 2023 at 15:00	1 hour
Outcomes assessed:

Assessment summary

Assignment: require students to integrate information from lectures and practice classes to create a concise written argument. Test your understanding of material covered in the vector calculus and differential equations components of the course.

Final Exam: cover all material in the unit from lectures, tutorials and practice classes.

Replacement Final Exam: if a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

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 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.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

Assignment: for late submission, every day (after due time) costs 20% of the original weight. Quiz: no late submission or replacement quiz will be accommodated. The weight can be moved to Final Exam after successful application through the University. Final Exam: subject to the university policy.

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.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

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
Multiple weeks	Review of partial differentiation techniques. Gradients, maxima, and minima, curves in space and the plane and the chain rule	Lecture and tutorial (8 hr)
	Multiple integration and their computation both in Euclidean and transcribed coordinates.	Lecture and tutorial (8 hr)
	Line integration and the main theorems of vector calculus	Lecture and tutorial (8 hr)
	Review of linear second order ordinary differential equations, methods for solving them and their applications	Lecture and tutorial (8 hr)
	Generalisation of the methods from second order linear equations to higher order equations.	Lecture and tutorial (8 hr)
	Advanced methods for solving linear ODEs.	Lecture and tutorial (8 hr)
	Fourier Series and applications to solving classical boundary value problems and PDEs	Lecture and tutorial (8 hr)
Weekly	Demonstration of interesting problems relating to the course material using the computer software package Mathematica	Lecture and tutorial (11 hr)

Attendance and class requirements

Class attendance is strongly recommended but not counted directly in course marks.

We plan to take partial attendance count in lectures and practice classes throughout the semester whenever possible for teaching data.

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 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

The unit will be based on a mixture of typed and (in-class) handwritten lecture notes provided throughout the semester. All lecture notes from Year 2022 will be provided at the beginning of the semester.

The following references are recommended but not required. All references for this unit can be accessed through the Library eReserve, available on Canvas.

Textbook: Calculus III, by Jerrold Marsden and Alan Weinstein. Undergraduate Texts in Mathematics. Springer-Verlag, New York. 1985.
Textbook: Elementary Differential Equations with Boundary Value Problems, by William F. Trench. Free Online edition 1.01 December 2013.

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. Demonstrate a conceptual understanding of vector-valued functions, partial derivatives, curves and integration over a region, volume and surface as well as solving basic differential equations with a background in a variet of techniques and applications of mathematical analysis.
LO2. Understand the definitions, main theorems, propositions, lemmata and corollaries for multivariate calculus as well as their applications to science. Also understand and the main theorems and methods of solving elementary linear differential equations as well as the applications.
LO3. Be fluent in the computation of integrals via substitution and coordinate transform methods.
LO4. Develop an appreiciation and strong working knowledge of the theory and applications of elementary vector analysis and differential equations.
LO5. Be fluent with important examples, theorems and applications and able to implement these in some computational supporting tool.
LO6. Present complete and mathematically rigorous solutions for problems in vector calculus and differential equations that include appropriate justification for their reasoning.
LO7. Recognise problems in mathematics and other areas of science and engineering that are amenable to mathematical analysis, and to apply the techniques of mathematical analysis in solving them.

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.

The assessment structure remains the same, with name and type revised according to university/faculty policy. It might be considered as "minor change".

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.

General Laboratory Safety Rules

No eating or drinking is allowed in any laboratory under any circumstances
A laboratory coat and closed-toe shoes are mandatory
Follow safety instructions in your manual and posted in laboratories
In case of fire, follow instructions posted outside the laboratory door
First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

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

MATH2921: Vector Calculus and Differential Eqs (Adv)

Semester 1, 2023 [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