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. 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).

Details

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

Prohibitions ?	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 and contact details

Coordinator	Mary Myerscough, mary.myerscough@sydney.edu.au
Lecturer(s)	Mary Myerscough , mary.myerscough@sydney.edu.au
Administrative staff	MATH1021@sydney.edu.au 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+)	Exam multiple choice and written calculations	60%	Formal exam period	1.5 hours
Outcomes assessed:
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:
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:
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:
Assignment	Webwork Online Quizzes online task (may require written calculations)	10%	Weekly	Weeks 2-7, 9-12
Outcomes assessed:
= 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	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.

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.

Weekly schedule

WK	Topic	Learning activity
Week 01	1. Set notation, the real number line; 2. Complex numbers in Cartesian form; 3. Complex plane, modulus	Lecture (2 hr)
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)
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)
Week 04	1. Definition of a limit; 2. Vertical and horizontal asymptotes; 3. The Squeeze Law; 4. Continuity	Lecture and tutorial (3 hr)
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)
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)
Week 07	1. Taylor polynomials; 2. The remainder term	Lecture and tutorial (3 hr)
Week 08	Taylor series	Lecture and tutorial (3 hr)
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)
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)
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)
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)
Week 13	Revision/further applications	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 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

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 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
Learning outcomes

Closing the loop

No changes have been made since this unit was last offered.

Additional information

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: https://edstem.org

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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Expectations of student conduct
Code of Conduct for Students, Conditions of Enrollment, University Privacy Statement, Academic Integrity
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Academic appeals process, special consideration, rules and guidelines, advice and support
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Policy register, policy search
Financial support
Scholarships, interest free loans, bursaries, money management
Study resources
Learning Centre, faculty and school programs, Library, online resources
Health and support
Student Centre, counselling & psychological services, University Health Service, general health and wellbeing

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

Details

Enrolment rules

Teaching staff and contact details

Assessment

Assessment criteria

Late submission

Special consideration

Academic integrity

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Graduate qualities

Outcome map

Closing the loop

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

MATH1021: Calculus Of One Variable

Overview

Details

Enrolment rules

Teaching staff and contact details

Assessment

Assessment criteria

Late submission

Special consideration

Academic integrity

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Graduate qualities

Outcome map

Closing the loop

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect