This is a course covering the elementary algebraic and calculus 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.

Learning Outcomes

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

 

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Develop critical thinking and problem solving skills, in the context of algebra and 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 sciences.
3. Explain the significance of the derivative and  integration and be able to apply techniques for the derivative and integration to situations in economics, engineering and sciences.
4.  Develop an appreciation of matrix models in economics, engineering and the physical, environmental and life sciences.

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

Precalculus 10th edition by Ron Larson (Cengage; metric edition).

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.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Linear Systems (7.2, 7.3) Gauss-Jordan Row Reduction (8.1) [Textbook references are shown in brackets - they refer to Precalculus 10th edition by Ron Larson.]	No assessment due
2	Matrix Algebra: sums and products (8.2) Matrix Algebra: inverses (8.3) Determinants (8.4) Cramer's Rule (8.5)	Online WebAssign quiz due at end of week
3	Functions: definition, graph of a function (1.4) Analyzing graphs of functions (1.5) Library of functions (1.6) Functions: graphing techniques, including transformations (1.7)	Online WebAssign quiz due at end of week In-workshop quiz
4	Quadratic functions and models (2.1) Polynomial Functions; Real and Complex Zeros (2.2, 2.4) Polynomial Division; Factor and Remainder Theorems (2.2, 2.4)	Online WebAssign quiz due at end of week In-workshop quiz Assignment 1 due
5	Rational Functions (2.6) Composite Functions (1.8) One-to-one Functions and Inverse Functions (1.9)	Online WebAssign quiz due at end of week In-workshop quiz
6	Exponential Functions, the number e (3.1) Logarithmic Functions, Properties of Logarithms (3.2, 3.3) Exponential and Logarithmic Equations (3.4) Exponential and Logarithmic Models (3.5)	Online WebAssign quiz due at end of teaching break 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	Angles and their measure (4.1) Trigonometric Functions (4.2, 4.3, 4.4) Graphs of Trigonometric Functions (4.5, 4.6)	Online WebAssign quiz due at end of week In-workshop quiz
8	Inverse Trigonometric Functions (4.7) Trigonometric Identities (5.1 - 5.5) Polar Coordinates (10.7) Polar Equations and Graphs (10.8)	Online WebAssign quiz due at end of week In-workshop quiz
9	(See also: Additional Notes on Vectors, on Wattle. References below to Chapter 12 and 13 are from this resource.) Vectors in two dimensions (6.3) Dot Product (6.4, 12.3) Vectors in three dimensions (12.1, 12.2) Cross Product (12.4)	Online WebAssign quiz due at end of week In-workshop quiz Assignment 2 due
10	Vector Equations: lines and planes (12.5, 13.1) (From this point on, we have gone beyond exercises in Larson: other sources will be recommended in lectures.) Limits and Continuity The Tangent Problem, Definition of the Derivative	Online WebAssign quiz due at end of week In-workshop quiz
11	Rules for Differentiation Applications of Differentiation Derivatives of Exponential and Logarithmic Functions Derivatives of Vector Functions	Online WebAssign quiz due at end of week In-workshop quiz
12	Related Rates Optimization The Second Derivative: inflection points, applications Review for the final exam	Online WebAssign quiz due at end of week In-workshop quiz

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 %	10/03/2019	02/06/2019	1,2,3,4
WebAssign Workbook	2 %	20/05/2019	09/06/2019	1,2,3,4
Workshop quizzes	8 %	12/03/2019	09/06/2019	1,2,3,4
Workshop Participation	2 %	12/03/2019	09/06/2019	1
Assignments (1 of 2)	5 %	18/03/2019	29/03/2019	1,2,4
Mid-semester exam	20 %	01/04/2019	03/05/2019	1,2,4
Assignments (2 of 2)	5 %	06/05/2019	24/05/2019	1,2
Final exam	50 %	06/06/2019	04/07/2019	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 check the ANU Examination Timetable to confirm the date, time and location of exams.

Assessment Task 1

11 Online Quizzes (homework)

Due at the end of each teaching week from Week 2 onwards (usually on Sunday nights), 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 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. 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)

See assessment task 5 for details.

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 most of the assessment tasks, no submission without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded. 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