This is a course covering the elementary methods necessary for mathematical modelling. Emphasis will be placed on developing facility, technique and use in applications. Modelling of processes and phenomena which occur in economics, engineering and the physical, environmental and life sciences will be used as a vehicle throughout. This course also provides a pathway to higher level mathematics courses.

The course will cover functions, trigonometric identities, vectors, limits, continuity, derivatives and integration.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Develop critical thinking and problem solving skills, in the context of calculus.
2. Describe the algebraic and graphical properties of elementary functions (linear, polynomial, exponential, logarithmic, trigonometric and their inverses) and their applications to engineering, economics and the sciences.
3. Explain the significance of the derivative and integration and be able to apply techniques for differentiation and integration to situations in economics, engineering and the sciences.
4. Understand the use of vectors in representing different coordinate systems.

Research-Led Teaching

Techniques covered in this course will be linked to applications in the physical and biological sciences, engineering and information technologies, economics and commerce.

Examination Material or equipment

A double sided A4 summary page (handwritten) is allowed in each of the exams.

Required Resources

Students need a computer to complete the online quizzes via the WebAssign platform, and to access Wattle (they can use either an ANU computer or they can use their own device).

Recommended Resources

Essential Calculus 2nd edition by James Stewart (Cengage). Our main reference text.

Precalculus 10th edition by Ron Larson (Cengage; metric edition). Optional but recommended: lectures will cover the material that is not in Stewart.

Read the text before the material is considered in lecture. This will increase your understanding of the material.

Staff Feedback

Students will be given written and verbal feedback as appropriate. Feedback may be provided to the whole course, to groups or to individuals.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

Where an assignment is formed of a number of activities, the date range indicates the due date for the first component and the return date of the final component. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site.

Adjustments to delivery in 2020

Course delivery and assessment in 2020 was adjusted due to the COVID-19 pandemic. Any information below that replaces what was published in the Class Summary for Semester 1, 2020 was approved by the Associate Dean Education (as is required after 10% commencement of a course). Where an activity or assessment is not referenced below, it remains unchanged.

Teaching Activities

• Lectures were pre-recorded and posted online.
• Workshops were done online.

Assessment

Adjustments were made to assignment due dates; for details see the course Wattle site.

• Midterm was cancelled.
• In-person Workshop quizzes cancelled.
• New weekly WebAssign Workshop Quiz worth 8%.
• New Assignment so there were three assignments at 5% each and 15% total.
• Final Exam was take home and worth 65%.    

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Functions Functions: Definition, Graph of a Function Analysing Graphs of Functions Library of Functions Graphing Techniques, including Transformations (Stewart 1.1, 1.2; Larson 1.4 - 1.7) [Textbook references are shown in brackets - they refer to Essential Calculus 2nd ed by James Stewart and Precalculus 10th ed by Ron Larson.]	No assessment due
2	Polynomial Functions Quadratic Functions and Models Polynomial Functions; Real and Complex Zeros Polynomial Division; Factor and Remainder Theorems (Larson 2.1 - 2.5)	Assignment 1 available Thursday
3	Composite Functions; Inverse Functions Rational Functions Composite Functions One-to-one Functions and Inverse Functions (Stewart 1.2, 5.1; Larson 2.6, 1.8, 1.9)	Online WebAssign quiz 1 due Tuesday In-workshop quiz
4	Exponential and Logarithmic Functions Exponential Functions, the Number e Logarithmic Functions, Properties of Logarithms Exponential and Logarithmic Equations Exponential and Logarithmic Models (Larson 3.1 - 3.5)	Online WebAssign quiz 2 due Monday Assignment 1 due Monday In-workshop quiz
5	Trigonometric and Inverse Trigonometric Functions Angles and their Measure Trigonometric Functions Graphs of Trigonometric Functions, Sinusoidal Curves Inverse Trigonometric Functions (Larson 4.1 - 4.7)	Online WebAssign quiz 3 due Monday In-workshop quiz
6	Trigonometric Identities; Polar Coordinates Trigonometric Identities Combining Waves; Applications Polar Coordinates Polar Equations and Graphs (Larson 5.1 - 5.5, 10.7, 10.8)	Online WebAssign quiz 4 due Monday In-workshop quiz Mid-semester exam (date to be confirmed; this exam is set centrally by the ANU in either Week 6 or 7: we will request Week 6)
7	Vectors Three Dimensional Coordinate Systems Vectors in Two and Three Dimensions Dot Product Vector Projection; Orthogonal Decomposition (Larson 6.3, 6.4; Stewart 10.1 - 10.3)	Online WebAssign quiz 5 due Monday In-workshop quiz Assignment 2 available Thursday
8	Limits and Continuity; The Derivative Limits Continuity Limits involving Infinity The Tangent Problem, Definition of the Derivative (Stewart 1.3 - 1.6, 2.1)	Online WebAssign quiz 6 due Monday In-workshop quiz
9	Derivatives Differentiation; Rates of Change Rules for Differentiation Derivatives of the Trigonometric Functions Product Rule, Quotient Rule, Chain Rule Implicit Differentiation (Stewart 2.1 - 2.6)	Online WebAssign quiz 7 due Monday Assignment 2 due Monday In-workshop quiz
10	Applications of the Derivative Related Rates First and Second Derivatives, the Shapes of Graphs Curve Sketching Optimisation (Stewart 2.7, 3.1, 3.3 - 3.5)	Online WebAssign quiz 8 due Monday In-workshop quiz
11	Integrals Antiderivatives The Area Problem; the Definite Integral Evaluating Definite Integrals: the Fundamental Theorem The Substitution Rule (Stewart 3.7, 4.1 - 4.5)	Online WebAssign quiz 9 due Monday In-workshop quiz
12	Applications of Integration Areas between Curves Volumes of Solids of Revolution Volumes by Slicing Review for the final exam (Stewart 7.1, 7.2)	Online WebAssign quiz 10 due Monday In-workshop quiz (Final Exam period begins Thursday of following week) (Online WebAssign quiz 11 due Monday of following week.)

Tutorial Registration

Workshops start in Week 3. Workshops are compulsory. If students do not attend a workshop, they get no marks for that workshop, including the in-class quiz for that week.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
11 Online Quizzes (homework)	8 %	10/03/2020	03/06/2020	1,2,3,4
WebAssign Workbook	2 %	18/05/2020	14/06/2020	1,2,3,4
Workshop quizzes	8 %	10/03/2020	14/06/2020	1,2,3,4
Workshop Participation	2 %	10/03/2020	14/06/2020	1
Assignments (1 of 2)	5 %	16/03/2020	27/03/2020	1,2,4
Mid-semester exam	20 %	30/03/2020	24/04/2020	1,2,4
Assignments (2 of 2)	5 %	04/05/2020	22/05/2020	1,2
Final exam	50 %	04/06/2020	02/07/2020	1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

Workshop participation is required. These workshops are the main place students can get individual help. Students are supported to work cooperatively and share ideas. They should write the solutions to questions on whiteboards so that the demonstrators can easily interact with students during the workshops.

Lecture attendance is highly encouraged; students who do not attend lectures are (statistically) more likely to have difficulties managing the required assessment. Lectures are routinely recorded through the Echo360 system and recordings are made available on the course Wattle page, however these should mostly be used for review purposes. Recordings are not a full substitute for regular lecture attendance.

Examination(s)

Mid-semester exam (worth 20%).

Final exam (worth 50%).

Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Assessment Task 1

11 Online Quizzes (homework)

Due at the beginning of each teaching week from Week 3 onwards (usually Monday), they are worth (in total) 8%. These are online quizzes that students complete in their own time. The quizzes are conducted using the WebAssign interface. The date range for these tasks indicates the approximate due date for the first quiz, and the approximate return date for the last quiz. Further details can be found on the course Wattle site.

Assessment Task 2

WebAssign Workbook

Students must keep a workbook (an exercise book of 80 pages or so) containing worked solutions to the Online Quizzes. This workbook is a very helpful resource when revising key concepts. The workshop demonstrators will look over and grade these workbooks in either Week 11 or Week 12. The workbook needs to be kept up to date over the course of the semester. The date range for this task indicates the approximate date for when the workbooks will be looked at, and the approximate date by which marks should be recorded on the course Wattle site.

Assessment Task 3

Workshop quizzes

A short quiz (approx 10 minutes) is set by the demonstrator at the beginning of each workshop. Graded quizzes will be returned to students in the following workshop (except for the quiz in Week 12 which will be returned during the same Week 12 workshop). The question(s) cover similar content to the online WebAssign quizzes due at the start of the week of the workshop. The date range for these tasks indicates the approximate date of the first workshop quiz, and the approximate date by which marks for the last quiz should be recorded on the course Wattle site.

Assessment Task 4

Workshop Participation

Students are required to work on weekly worksheets, and are highly encouraged to work cooperatively in groups (ideally at a whiteboard). The groups write solutions to questions on their whiteboards so that workshop demonstrators can easily review and interact with their work. Each week an individual or group of students may be asked to present solutions to specified questions at the end of the workshop: completion of this task at least once during the semester will contribute to a student's participation score. The date range for this task indicates the approximate date of the first workshop, and the approximate date by which marks should be recorded on the course Wattle site.

Assessment Task 5

Assignments (1 of 2)

These assignments are designed to build skills in interpretation, mathematical technique and clear mathematical expression and will be graded accordingly. Students must clearly justify their reasoning to explain how they arrived at their answers. If there is no explanation and there are no intermediate steps shown in the answer to a particular question, it will be given no marks.

Assessment Task 6

Mid-semester exam

This written exam is scheduled centrally by the ANU in either Week 6 or Week 7. It will normally be of two hours in length, covering content in the 5 or 6 weeks of the course as appropriate. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location of the mid-semester exam.

Assessment Task 7

Assignments (2 of 2)

These assignments are designed to build skills in interpretation, mathematical technique and clear mathematical expression and will be graded accordingly. Students must clearly justify their reasoning to explain how they arrived at their answers. If there is no explanation and there are no intermediate steps shown in the answer to a particular question, it will be given no marks.

Assessment Task 8

Final exam

This written exam is scheduled centrally by the ANU at the end of semester. It will normally be of three hours in length, covering the entire course. In order to pass the course, a student must achieve at least 40% of the marks available on the exam. If this hurdle requirement is not satisfied, where a student would otherwise have passed the course, they will be awarded an overall PX grade and offered a supplementary exam in accordance with ANU policies. Please check the ANU final Examination Timetable to confirm the date, time and location of the end of semester exam.

Academic Integrity

Academic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.

Online Submission

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

For the two assignments only, late submission without an extension will be penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of the two assignments will not be accepted after a date to be specified when the assignment is set.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Marked assignments will be returned via Wattle.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Students cannot resubmit their assignments.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information. In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service — including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy. If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes. Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students