Outline

Overview

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. 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 complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals. Additional theoretical topics included in this advanced unit include the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem. Students are strongly recommended to complete MATH1021 Calculus Of One Variable 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

Academic unit	Mathematics and Statistics Academic Operations
Credit points	3
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	MATH1001 or MATH1906 or ENVX1001 or MATH1901 or MATH1021 or MATH1931
Assumed knowledge ?	(HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Milena Radnovic, milena.radnovic@sydney.edu.au

Type	Description	Weight	Due	Length
Supervised exam ?	Final exam written calculations and multiple choice	60%	Formal exam period	1.5 hours
Outcomes assessed:
Assignment	Assignment 1 written calculations	5%	Week 04 Due date: 16 Mar 2023 at 23:59 Closing date: 26 Mar 2023	3-5 pages (as a guide)
Outcomes assessed:
Online task	Quiz 1 Multiple choice or short answer questions	11.5%	Week 07 Due date: 06 Apr 2023 at 23:59 Closing date: 06 Apr 2023	40 minutes
Outcomes assessed:
Assignment	Assignment 2 written calculations	10%	Week 09 Due date: 27 Apr 2023 at 23:59 Closing date: 07 May 2023	6-8 pages (as a guide)
Outcomes assessed:
Online task	Quiz 2 Multiple choice or short answer questions	11.5%	Week 12 Due date: 18 May 2023 at 23:59 Closing date: 18 May 2023	40 minutes
Outcomes assessed:
Participation	Tutorials Participation in tutorials	2%	Weekly	50 minutes/week
Outcomes assessed:

Assessment summary

Assignments: There are two assignments, which must be submitted electronically, as PDF files 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. Penalties apply for late submission. 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.
Quizzes: The quizzes will be held online through Canvas. Each 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 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.
Tutorial Participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class activities during the tutorials. It is 0.25 marks per tutorial class up to 8 tutorials (there are 12 tutorials).
Final Examination: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. Further information about the exam will be made available at a later date on Canvas. 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	At HD level, a student demonstrates a flair for the subject as well as a detailed and comprehensive understanding of the unit material. A ‘High Distinction’ reflects exceptional achievement and is awarded to a student who demonstrates the ability to apply their subject knowledge and understanding to produce original solutions for novel or highly complex problems and/or comprehensive critical discussions of theoretical concepts.
Distinction	75 - 84	At DI level, a student demonstrates an aptitude for the subject and a well-developed understanding of the unit material. A ‘Distinction’ reflects excellent achievement and is awarded to a student who demonstrates an ability to apply their subject knowledge and understanding of the subject to produce good solutions for challenging problems and/or a reasonably well-developed critical analysis of theoretical concepts.
Credit	65 - 74	At CR level, a student demonstrates a good command and knowledge of the unit material. A ‘Credit’ reflects solid achievement and is awarded to a student who has a broad general understanding of the unit material and can solve routine problems and/or identify and superficially discuss theoretical concepts.
Pass	50 - 64	At PS level, a student demonstrates proficiency in the unit material. A ‘Pass’ reflects satisfactory achievement and is awarded to a student who has threshold knowledge.
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.

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
Week 01	Complex numbers in Cartesian and polar form. Complex powers and De Moivre’s Theorem.	Lecture (2 hr)
Week 02	The complex exponential function, n-th roots. Representing complex functions.	Lecture and tutorial (3 hr)
Week 03	Injective and bijective functions. Inverse functions. Hyperbolic functions.	Lecture and tutorial (3 hr)
Week 04	Limits and the limit laws.	Lecture and tutorial (3 hr)
Week 05	Continuity. Intermediate Value Theorem.	Lecture and tutorial (3 hr)
Week 06	Differentiability. Rolle’s Theorem and the Mean Value Theorem.	Lecture and tutorial (3 hr)
Week 07	Cauchy’s Mean Value Theorem and L’Hopital’s Rule.	Lecture and tutorial (3 hr)
Week 08	Taylor polynomials with remainder, Taylor series of standard functions.	Lecture and tutorial (3 hr)
Week 09	Evaluation of Riemann sums. Definition of the Riemann integral.	Lecture and tutorial (3 hr)
Week 10	Fundamental Theorem of Calculus. Functions defined by integrals.	Lecture and tutorial (3 hr)
Week 11	Applications of Riemann sums and integrals: for instance volumes, arc lengths, volumes of revolution, surface area of revolution.	Lecture and tutorial (3 hr)
Week 12	Improper integrals Integrals of unbounded functions. Integrals over unbounded intervals. Comparison tests.	Lecture and tutorial (3 hr)
Week 13	Revision / Spill-over	Lecture and tutorial (3 hr)

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 and participation will be recorded to determine the participation mark. Your attendance will not be recorded unless you attend the tutorial in which you are enrolled. We strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions.

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 for MATH1921 Calculus of One Variable (Advanced) are available for purchase from Kopystop, 55 Mountain St, Broadway.

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, and express mathematical ideas coherently using precise mathematical language.
LO2. demonstrate fluency in the mathematical manipulation of complex numbers and functions, including concepts of surjectivity, injectivity and inverse functions
LO3. understand and be able to use fundamental properties of continuous and differentiable functions including limits, limit laws, intermediate and extreme value theorems as well as mean value theorems and applications
LO4. work with Taylor polynomial approximations and Taylor series representations of functions including dealing with remainder estimates
LO5. demonstrate an understanding of the definition and computation or estimation of definite, indefinite and improper Riemann integrals including proficiency in using integration methods without too much guidance
LO6. understand and be able to use the relationships between integral and differential calculus via the Fundamental Theorem of Calculus
LO7. apply concepts of calculus to a variety of contexts and applications

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.

Small tutorial participation mark added with a consequent reduction in the quiz weightings.

Additional information

Lectures: Lectures are face-to-face and streamed live with online access from Canvas.
Tutorials: Tutorials start in week 2. 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.
Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1921 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: https://edstem.org

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

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

MATH1921: Calculus Of One Variable (Advanced)

Semester 1, 2023 [Normal day] - Remote

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

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect