Unit of study_

# MATH1011: Applications of Calculus

## Overview

This unit is designed for science students who do not intend to undertake higher year mathematics and statistics. It establishes and reinforces the fundamentals of calculus, illustrated where possible with context and applications. Specifically, it demonstrates the use of (differential) calculus in solving optimisation problems and of (integral) calculus in measuring how a system accumulates over time. Topics studied include the fitting of data to various functions, the interpretation and manipulation of periodic functions and the evaluation of commonly occurring summations. Differential calculus is extended to functions of two variables and integration techniques include integration by substitution and the evaluation of integrals of infinite type.

### Details

Academic unit Mathematics and Statistics Academic Operations MATH1011 Applications of Calculus Semester 1, 2020 Normal day Camperdown/Darlington, Sydney 3

### Enrolment rules

 Prohibitions ? MATH1001 or MATH1901 or MATH1906 or BIOM1003 or ENVX1001 or MATH1021 or MATH1921 or MATH1931 None None HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Please note: this unit does not normally lead to a major in Mathematics or Statistics or Financial Mathematics and Statistics. Yes

### Teaching staff and contact details

Coordinator Daniel Daners, daniel.daners@sydney.edu.au Clio Cresswell Brad Roberts MATH1011@sydney.edu.au

## Assessment

Type Description Weight Due Length
Final exam Final Exam
written calculations and multiple choice
65% Formal exam period 1.5 hours
Outcomes assessed:
Assignment Assignment 1
written calculations
2.5% Week 04
Due date: 19 Mar 2020 at 23:59

Closing date: 29 Mar 2020
10 days
Outcomes assessed:
Tutorial quiz Quiz 1
written calculations
15% Week 07 40 Minutes
Outcomes assessed:
Assignment Assignment 2
written calculations
2.5% Week 09
Due date: 30 Apr 2020 at 23:59

Closing date: 10 May 2020
10 days
Outcomes assessed:
Tutorial quiz Quiz 2
written calculations
15% Week 12 40 Minutes
Outcomes assessed:

Below are brief assessment details. Further information can be found in the Canvas site for this unit.

• Assessments: There are two assignments, which must be submitted electronically, as PDF files only, in 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.

### 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.

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.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 Periodicity. Lecture (2 hr)
Week 02 Scaling Data. Lecture and tutorial (3 hr)
Week 03 Scaling Data and Finite Differences. Lecture and tutorial (3 hr)
Week 04 Optimisation: One Variable Problems. Lecture and tutorial (3 hr)
Week 05 Optimisation: One Variable Problems (continued). Lecture and tutorial (3 hr)
Week 06 Optimisation: Two Variable Problems. Lecture and tutorial (3 hr)
Week 07 Optimisation: Two Variable Problems (continued). Lecture and tutorial (3 hr)
Week 08 Method of Least Squares. Lecture and tutorial (3 hr)
Week 09 Finite Sums. Lecture and tutorial (3 hr)
Week 10 The Definite Integral. Lecture and tutorial (3 hr)
Week 11 The Indefinite Integral. Lecture and tutorial (3 hr)
Week 12 Applications of Integration. Lecture and tutorial (3 hr)
Week 13 Revision. Lecture and tutorial (3 hr)

### 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.

• Applications of Calculus (Course Notes for MATH1011) are available for purchase from Kop ystop, 55 Mountain St, Broadway.
• Reference book: James Stewart. Calculus. Cengage Learning. 8th Edition, Metric Version, 2015, ISBN 978-1-305-26672-8.
Available from the Co-op Bookshop.

## 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. analyse practical problems using techniques from differential and integral calculus;
• LO2. fit as appropriate a linear, polynomial, exponential or a periodic function to a set of experimental data;
• LO3. sketch the generalised sinusoidal functions;
• LO4. use differential calculus to solve optimisation problems in one independent variable;
• LO5. calculate the partial derivatives of functions of two variables, and hence to solve optimisation problems in two independent variables;
• LO6. calculate finite sums and use the sigma notation where appropriate;
• LO7. evaluate definite integrals and use definite integrals in applications;
• LO8. determine when improper integrals of infinite type exist.

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

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Closing the loop

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