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Unit of study_

MATH1021: Calculus Of One Variable

Semester 1, 2020 [Normal day] - Camperdown/Darlington, Sydney

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.

Unit details and rules

Unit code MATH1021
Academic unit Mathematics and Statistics Academic Operations
Credit points 3
Prohibitions
? 
MATH1011 or MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931
Prerequisites
? 
None
Corequisites
? 
None
Assumed knowledge
? 

HSC Mathematics Extension 1 or equivalent.

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Daniel Daners, daniel.daners@sydney.edu.au
Lecturer(s) Behrouz Taji, behrouz.taji@sydney.edu.au
Daniel Hauer, daniel.hauer@sydney.edu.au
Mary Myerscough, mary.myerscough@sydney.edu.au
Fernando Viera, fernando.viera@sydney.edu.au
Type Description Weight Due Length
Final exam Exam
written calculations and multiple choice
55% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO15 LO14 LO13 LO12 LO11 LO10 LO9 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 1
written calculations submitted online
2.5% Week 04
Due date: 19 Mar 2020 at 23:59

Closing date: 29 Mar 2020
10 days
Outcomes assessed: LO1 LO4 LO3 LO2
Tutorial quiz Quiz 1
written calculations
15% Week 07 40 minutes
Outcomes assessed: LO1 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 2
written calculations submitted online
2.5% Week 09
Due date: 07 May 2020 at 23:59

Closing date: 17 May 2020
10 days
Outcomes assessed: LO7 LO10 LO9 LO8
Tutorial quiz Quiz 2
written calculations
15% Week 12 40 minutes
Outcomes assessed: LO8 LO12 LO11 LO10 LO9
Assignment Webwork online quizzes
online task (may require written calculations)
10% Weekly Weeks 2-13
Outcomes assessed: LO1

Assessment summary

  • 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.
  • 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, granted 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.
  • Online quizzes: There are twelve weekly online quizzes. Each online quiz consists of a set of randomized questions. The
    best 10 of your 12 quizzes will count, making each worth 1%. 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 quizzes will come from your exam. The deadline for completion of each quiz is 11:59 pm Thursday (starting in week 2). We recommend that you follow the due dates outlined above to gain the most benefit from these quizzes.
  • Examination: 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 the website.

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 sydney.edu.au/students/guide-to-grades.

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.

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.

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.

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 Lecture and tutorial (3 hr) LO3 LO4 LO5
Week 03 1. Definition of e^iθ and e^z for z complex; 2. Applications to trigonometry; 3. Revision of domain and range of a function Lecture and tutorial (3 hr) LO5
Week 04 1. Limits and continuity; 2. Vertical and horizontal asymptotes Lecture and tutorial (3 hr) LO6
Week 05 1. Differentiation and the chain rule; 2. Implicit differentiation; 3. Hyperbolic and inverse functions Lecture and tutorial (3 hr) LO8
Week 06 1. Optimising and sketching functions of one variable; 2. Linear approximations and differentials; 3. L’Hopital’s rule Lecture and tutorial (3 hr) LO7 LO9
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. Riemann sums; 2. Definition of definite integral; 3. Non-positive functions Lecture and tutorial (3 hr) LO11 LO12
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. Integration by parts; 3.Trigonometric substitutions Lecture and tutorial (3 hr) LO13
Week 12 1. Areas and volumes by slicing; 2. The disk and shell methods Lecture and tutorial (3 hr) LO12
Week 13 Revision Lecture and tutorial (3 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 LO12 LO13 LO14 LO15

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 are available for purchase from Kopystop, 55 Mountain St, Broadway.
  • See the Junior Mathematics Handbook for other useful references.
     

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

This section outlines changes made to this unit following staff and student reviews.

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.

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.