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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 of MATH1921 before commencing MATH1023 or MATH1923.


Academic unit Mathematics and Statistics Academic Operations
Unit code MATH1021
Unit name Calculus Of One Variable
Session, year
Intensive February, 2021
Attendance mode Block mode
Location Camperdown/Darlington, Sydney
Credit points 3

Enrolment rules

MATH1011 or 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 Daniel Hauer,
Lecturer(s) Daniel Hauer ,
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
Assignment Webwork Online Quizzes
online task (may require written calculations)
8% Progressive weeks 1-4
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14 LO15
Assignment Assignment 1
written calculations
4% Week 02
Due date: 25 Jan 2021 at 23:59

Closing date: 01 Feb 2021
7 days
Outcomes assessed: LO1 LO2 LO3 LO4
Assignment Assignment 2
written calculations
8% Week 04
Due date: 08 Feb 2021 at 23:59

Closing date: 15 Feb 2021
7 days
Outcomes assessed: LO1 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Final exam (Open book) Type C final exam Final Exam
Online open book without invigilation
65% Week 05
Due date: 19 Feb 2021 at 13:00
1.5 hours
Outcomes assessed: LO1 LO15 LO14 LO13 LO12 LO11 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Online task Quiz
Multiple choice or written calculations
15% Week 05
Due date: 17 Feb 2021 at 12:00
40 minutes
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14 LO15
Type C final exam = Type C 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.
  • Webwork Online Quizzes: There are ten online quizzes (2 in week 1, 3 in week 2 & 3, and 2 in week 4). 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! But 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 of each teaching day (starting in week 1). The precise schedule for the quizzes is found on Canvas.
  • Quizzes: One 40 minutes Canvas quiz will be held in week 5 during the regular tutoral time. Due dates are specified on Canvas. There is not need to apply for special consideration since the better mark principle will be used for 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.
  • Examination: At the end of week 5 of the Intensive February Session 2021, a final exam will be held online via Canvas. 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


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 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.

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 Block teaching (2 hr) LO1 LO2 LO3
1. Complex numbers in polar form; 2. De Moivre’s theorem; 3. Complex powers and nth roots Block teaching (2 hr) LO3 LO4 LO5
1. Definition of e^iθ and e^z for z complex; 2. Applications to trigonometry; 3. Revision of domain and range of a function Block teaching (2 hr) LO5
Week 02 1. Limits and continuity; 2. Vertical and horizontal asymptotes Block teaching (2 hr) LO6
1. Differentiation and the chain rule; 2. Implicit differentiation; 3. Hyperbolic and inverse functions Block teaching (2 hr) LO8
1. Optimising and sketching functions of one variable; 2. Linear approximations and differentials; 3. L’Hopital’s rule Block teaching (2 hr) LO7 LO9
Week 03 1. Taylor polynomials; 2. The remainder term Block teaching (2 hr) LO10
Taylor series Block teaching (2 hr) LO10
1. Riemann sums; 2. Definition of definite integral; 3. Non-positive functions Block teaching (2 hr) LO11 LO12
Week 04 1. Fundamental theorem of calculus (parts 1 and 2); 2. Functions defined by integrals; 3. Natural logarithm and exponential functions Block teaching (2 hr) LO14
1. Integration by substitution; 2. Integration by parts; 3.Trigonometric substitutions Block teaching (2 hr) LO13
1. Areas and volumes by slicing; 2. The disk and shell methods Block teaching (2 hr) LO12

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.

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.

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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