Unit outline_

# MATH1021: Calculus Of One Variable

## 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).

### Unit details and rules

Academic unit Mathematics and Statistics Academic Operations 3 None None MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 HSC Mathematics Extension 1 or equivalent No

### Teaching staff

Coordinator Daniel Hauer, daniel.hauer@sydney.edu.au Daniel Hauer

## Assessment

Type Description Weight Due Length
Online task Webwork Online Quizzes
online task (may require written calculations)
10% Progressive weeks 1-4
Outcomes assessed:
Assignment Assignment 1
written calculations
5% Week 02
Due date: 23 Jan 2022 at 23:59

Closing date: 30 Jan 2022
7 days
Outcomes assessed:
Assignment Assignment 2
written calculations
10% Week 04
Due date: 06 Feb 2022 at 23:59

Closing date: 13 Feb 2022
7 days
Outcomes assessed:
Multiple choice or written calculations
15% Week 05
Due date: 08 Feb 2022 at 12:00
40 minutes
Outcomes assessed:
Final exam (Record+) Final Exam
Multiple choice and written calculations.
60% Week 06
Due date: 16 Feb 2022 at 12:00
1.5 hours
Outcomes assessed:
= Type B final exam

### Assessment summary

• 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.
• 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 7 days past the original due date. Further extensions past this time will not be permitted. The better mark principle does not apply on assignments!
• Webwork Online Quizzes: There are ten online quizzes. Each online quiz consists of a set of randomized questions. The best 8 out of your 10 quizzes will count, making 10% of your total mark. You cannot apply for special consideration for a single webwork quiz! But 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. The deadline for completion of each quiz is three days later counted from the opening day.
• Examination: In week 6 of the intensive session, a final exam will be held online. 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

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.

### 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.

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.

## Learning support

### 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.

## Weekly schedule

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)
1. Complex numbers in polar form; 2. De Moivre’s theorem; 3. Complex powers and nth roots Block teaching (2 hr)
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)
Week 02 1. Limits and continuity; 2. Vertical and horizontal asymptotes Block teaching (2 hr)
1. Differentiation and the chain rule; 2. Implicit differentiation; 3. Hyperbolic and inverse functions Block teaching (2 hr)
1. Optimising and sketching functions of one variable; 2. Linear approximations and differentials; 3. L’Hopital’s rule Block teaching (2 hr)
Week 03 1. Taylor polynomials; 2. The remainder term Block teaching (2 hr)
Taylor series Block teaching (2 hr)
1. Riemann sums; 2. Definition of definite integral; 3. Non-positive functions Block teaching (2 hr)
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)
1. Integration by substitution; 2. Integration by parts; 3.Trigonometric substitutions Block teaching (2 hr)
1. Areas and volumes by slicing; 2. The disk and shell methods Block teaching (2 hr)

### 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 on-campus or online tutorials/workshops/laboratories have been scheduled, students should make every effort to attend and participate at the scheduled time. If you are unable to attend for any reason (e.g. health or technical issues) you should and attend another session, if available. Penalties will not apply if you cannot attend your scheduled class.

• Attendance: Students are expected to attend a minimum of 80% of timetabled activities for a unit of study, unless granted exemption by the Associate Dean. For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%.
• 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.

• 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.

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.

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

## Responding to student feedback

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

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