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Unit outline_

MATH1921: Calculus Of One Variable (Advanced)

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. Additional theoretical topics included in this advanced unit include the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 3
Prerequisites
? 
None
Corequisites
? 
None
Prohibitions
? 
MATH1001 or MATH1011 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 Daniel Daners, daniel.daners@sydney.edu.au
Lecturer(s) Daniel Daners, daniel.daners@sydney.edu.au
Type Description Weight Due Length
Final exam Final exam
written calculations and multiple choice
70% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7
Assignment Assignment 1
written calculations
5% Week 04
Due date: 19 Mar 2020 at 23:59

Closing date: 29 Mar 2020
10 days
Outcomes assessed: LO1 LO2
Tutorial quiz Quiz 1
written calculations
10% Week 07 40 Minutes
Outcomes assessed: LO1 LO3 LO2
Assignment Assignment 2
written calculations
5% Week 09
Due date: 30 Apr 2020 at 23:59

Closing date: 10 May 2020
10 days
Outcomes assessed: LO1 LO2 LO3 LO4 LO7
Tutorial quiz Quiz 2
written calculations
10% Week 12 40 Minutes
Outcomes assessed: LO1 LO7 LO6 LO5 LO4 LO3 LO2

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.
  • 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, issued 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.
  • Examination: Further information about the exam will be made available at a later date 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

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.

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 Complex numbers in Cartesian and polar form. Complex powers and De Moivre’s Theorem. Lecture (2 hr) LO1 LO2
Week 02 The complex exponential function, n-th roots. Representing complex functions. Lecture and tutorial (3 hr) LO1 LO2
Week 03 Injective and bijective functions. Inverse functions. Hyperbolic functions. Lecture and tutorial (3 hr) LO1 LO2 LO3
Week 04 Limits and the limit laws. Lecture and tutorial (3 hr) LO1 LO3
Week 05 Continuity. Intermediate Value Theorem. Lecture and tutorial (3 hr) LO1 LO3
Week 06 Differentiability. Rolle’s Theorem and the Mean Value Theorem. Lecture and tutorial (3 hr) LO1 LO3
Week 07 Cauchy’s Mean Value Theorem and L’Hopital’s Rule. Lecture and tutorial (3 hr) LO1 LO3
Week 08 Taylor polynomials with remainder, Taylor series of standard functions. Lecture and tutorial (3 hr) LO1 LO4
Week 09 Evaluation of Riemann sums. Definition of the Riemann integral. Lecture and tutorial (3 hr) LO1 LO5
Week 10 Fundamental Theorem of Calculus. Functions defined by integrals. Lecture and tutorial (3 hr) LO1 LO5 LO6
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) LO1 LO5 LO7
Week 12 Improper integrals Integrals of unbounded functions. Integrals over unbounded intervals. Comparison tests. Lecture and tutorial (3 hr) LO1 LO7
Week 13 Revision / Spill-over Lecture and tutorial (3 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7

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

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 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
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.
  • Tutorial and Exercise Sheets: The question sheets for a given week will be available on the MATH1921 webpage. Solutions to tutorial exercises for week n will usually be posted on the web by the afternoon of the Friday on week n.
  • Ed Discussion forum accessible through Canvas

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.