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Unit of study_

MATH1021: Calculus Of One Variable

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. Students are strongly recommended to complete MATH1021 or MATH1921 Calculus Of One Variable (Advanced) before commencing MATH1023 Multivariable Calculus and Modelling or MATH1923 Multivariable Calculus and Modelling (Adv).


Academic unit Mathematics and Statistics Academic Operations
Unit code MATH1021
Unit name Calculus Of One Variable
Session, year
Semester 1, 2022
Attendance mode Normal day
Location Remote
Credit points 3

Enrolment rules

MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931
Assumed knowledge

HSC Mathematics Extension 1 or equivalent

Available to study abroad and exchange students


Teaching staff and contact details

Coordinator Mary Myerscough,
Lecturer(s) Mary Myerscough ,
Administrative staff Please send all email regarding MATH1021 to this address. It goes to the unit of study coordinator, the lecturers and administrative support.
Type Description Weight Due Length
Final exam (Record+) Type B final exam Exam
multiple choice and written calculations
60% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14 LO15
Assignment Assignment 1
written calculations
5% Week 04
Due date: 17 Mar 2022 at 23:59

Closing date: 27 Mar 2022
10 days
Outcomes assessed: LO1 LO4 LO3 LO2
Online task Quiz
multiple choice or written calculations
15% Week 08
Due date: 14 Apr 2022 at 23:59

Closing date: 14 Apr 2022
40 minutes
Outcomes assessed: LO2 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3
Assignment Assignment 2
written calculations
10% Week 11
Due date: 12 May 2022 at 23:59

Closing date: 22 May 2022
10 days
Outcomes assessed: LO1 LO12 LO11 LO10 LO9 LO8 LO7
Assignment Webwork Online Quizzes
online task (may require written calculations)
10% Weekly Weeks 2-7, 9-12
Outcomes assessed: LO1 LO14 LO13 LO12 LO11 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3
Type B final exam = 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 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 is worth 1% and consists of a set of randomized questions. You cannot apply for special consideration for the quizzes. The better mark principle will apply for the total 10% - i.e. if your overall exam mark is higher, then your 10% for the Webwork quizzes will come from your exam. he deadline for completion of each quiz is 23:59 Thursday (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. 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.
  • Simple Extensions: No simple extensions are given in first year units in the School of Mathematics and Statistics. 

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


High distinction

85 - 100

Representing complete or close to complete mastery of the material.


75 - 84

Representing excellence, but substantially less than complete mastery.


65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.


50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.


0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see

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.

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.

WK Topic Learning activity Learning outcomes
Week 01 1. Set notation, the real number line; 2. Complex numbers in Cartesian form; 3. Complex plane, modulus Lecture (2 hr) LO2 LO3
Week 02 1. Complex numbers in polar form; 2. De Moivre’s theorem; 3. Complex powers and nth roots 4. Roots of polynomials 5. The complex exponential. Lecture and tutorial (3 hr) LO1 LO3 LO4 LO5
Week 03 1. Definition, domain and range of a function 2. Composite and inverse functions 3. Inverse trigonometric functions 4. Hyperbolic functions Lecture and tutorial (3 hr) LO5
Week 04 1. Definition of a limit; 2. Vertical and horizontal asymptotes; 3. The Squeeze Law; 4. Continuity Lecture and tutorial (3 hr) LO1 LO6 LO15
Week 05 1. The derivative as a rate of change; 2. Formal definition of the derivative; 3. The Chain Rule; 4. Implicit differentiation; 5. The Mean Value Theorem Lecture and tutorial (3 hr) LO1 LO6 LO15
Week 06 1. Optimising and sketching functions of one variable; 2. Concavity; 3. Curve sketching; 4. L’Hopital’s rule Lecture and tutorial (3 hr) LO1 LO7 LO9 LO15
Week 07 1. Taylor polynomials; 2. The remainder term Lecture and tutorial (3 hr) LO10
Week 08 Taylor series Lecture and tutorial (3 hr) LO10
Week 09 1. The integral as a measure of accumulation; 2. Riemann sums; 3. Definition of definite integral; 4. Properties of Riemann integrals Lecture and tutorial (3 hr) LO1 LO11 LO12 LO15
Week 10 1. Fundamental theorem of calculus (parts 1 and 2); 2. Functions defined by integrals; 3. Natural logarithm and exponential functions Lecture and tutorial (3 hr) LO14
Week 11 1. Integration by substitution; 2. Partial fraction decomposition; 3. Integration by parts; 4.Trigonometric integrals; 5. Reduction formulae. Lecture and tutorial (3 hr) LO1 LO13
Week 12 1. Areas and volumes by slicing; 2. The disk and shell methods; 3. Using incremental lengths to find the arc length of a function. Lecture and tutorial (3 hr) LO12 LO15
Week 13 Revision/further applications Lecture and tutorial (3 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14

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 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 for MATH1021 Calculus of One Variable (available on Canvas)
  • See the Canvas site for more reference material.

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 rigour to solve problems
  • LO2. read and write basic set notation
  • LO3. demonstrate competency in arithmetic operations with complex numbers in Cartesian, polar, and exponential form
  • LO4. use de Moivre’s theorem to find powers and roots of complex numbers
  • LO5. solve simple polynomial equations involving complex numbers
  • LO6. apply an intuitive understanding of a limit and knowledge of basic limit laws to calculate the limits of functions
  • LO7. use the differential of a function to calculate critical points and apply them to optimise functions of one variable
  • LO8. find inverse functions
  • LO9. use L’Hopital’s rule to find limits of indeterminate forms
  • LO10. find Taylor polynomials and the Taylor series expansion of a function
  • LO11. approximate definite integrals by finite sums and vice versa
  • LO12. express areas, and volumes of revolution, as definite integrals
  • LO13. apply standard integration techniques to find anti-derivatives and definite integrals
  • LO14. determine properties of a function defined by an integral using the graph of its integrand
  • LO15. express mathematical ideas and arguments coherently in written form.

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
No changes have been made since this unit was last offered.
  • Lectures: Lectures are online and live. Access from Canvas.
  • Tutorials: 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.
  • Tutorials: Tutorials 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. If you are absent from a tutorial do not apply for Special Consideration or Special Arrangement, since there is no assessment associated with the missed tutorial.
  • Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1021 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:

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.


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