This course provides a study of the fundamental concepts of calculus and linear algebra. The use and understanding of proof and abstract ideas, will allow students to develop analytical skills which will form a foundation for further study in the quantitative areas of actuarial studies.

Topics to be covered include: Calculus - limits, continuity, differentiation, inverse functions, transcendental functions, extrema, concavity and inflections, applications of derivatives, Taylor Polynomials, integration, differential equations, functions of several variables, partial derivatives, optimality, gradient and the second derivative test in two variables, double integrals; Linear Algebra - complex numbers, solving linear equations, matrix equations, linear independence, linear transformations, matrix operations, matrix inverses, subspaces, dimension and rank, determinants, Cramer's rule, volumes, eigenvalues, eigenvectors.

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. Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts. (LO1)
2. Demonstrate accurate and efficient use of calculus and linear algebra techniques. (LO2)
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from calculus and linear algebra. (LO3)
4. Apply problem-solving using calculus and linear algebra techniques applied to situations in statistics, physics, engineering and other mathematical contexts. (LO4)

Examination Material or equipment

Although circumstances may change, at the moment it is intended that you will need a zoom-capable environment in which to take your exams, and the ability to quickly scan or otherwise create a .pdf document for submission.

Required Resources

The lecture material and assigned problems for this course are self-contained. Purchasing textbooks is not mandatory. However, you may wish to read a textbook regularly as a companion to the lecture material or as a source of extra worked examples and problems. For this reason, we have chosen two texts. Each text is available from the ANU library. You may be able to use earlier editions of the text, and there are many other texts covering the same material. For each course topic, references to the appropriate sections of the prescribed textbooks (see below) will be given so that you can look up these texts if you wish.

The prescribed textbook for the linear algebra part of the course is:

Title: Linear algebra and its applications,

Authors: David Lay; with Steven R. Lay and Judi J. McDonald.

Edition: Fifth edition, Global edition.

Publication details:Harlow, Essex : Pearson Education Limited, 2016.

Paperback ISBN: 9781292092232

ebook ISBN: 9780134013473

The prescribed textbook for the calculus part of the course is:

Title: Essential Calculus

Author: James Stewart

Edition: Second edition.

Paperback ISBN: 9781133490944

ebook ISBN: 9780357539316

Recommended Resources

Recommended student system requirements 

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments during workshops and consultation
• feedback to the whole class, groups, individuals, focus group etc

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.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Systems of linear equations; Gaussian elimination and row echelon forms; Applications of linear systems; Vectors and vector operations, Matrix-vector products.	No workshops in Week 1
2	Solution sets of linear systems; Linear independence; Subspaces and basis of a subspace; Dimension of subspaces	Workshop LA1; Assignment LA1 released
3	Inner products and orthogonality; Linear transformations, The matrix of a linear transformation; Matrix multiplication and other algebraic operations; Matrix inverses .	Workshop LA2; Assignment LA2 released
4	Characteristics of invertible matrices/invertible linear transformations; Determinants and their properties; Cramer's rule, determinant formula, and areas; Eigenvalues and eigenvectors.	Workshop LA3; Assignment LA3 released
5	Characteristic polynomial; Diagonalisation; Eigenvectors and linear transformations; Complex numbers.	Workshop LA4; Assignment LA4 released
6	Complex eigenvectors; Dynamical systems. Functions, limits and the Squeeze Theorem, Continuity; Related rates and linear approximations.	Workshop LA5; Assignment LA5 released
7	Derivatives, rates of change and basic differentiation rules, Minimum and Maximum values, Mean Value Theorem, Shape of graphs, l’Hospital’s Rule, Curve Sketching, Optimisation Problems;	No workshops in Week 7
8	Antiderivatives; Definite integral, Evaluating Definite Integrals; Fundamental Theorem of Calculus; Inverse functions, logarithmic and exponential functions.	Workshop C1; Assignment C1 released
9	Integration techniques: by substitutions and by parts; Trigonometric integrals and improper integrals. Integration for partial fractions, Exponential Growth and Decay. Differential equations.	Workshop C2; Assignment C2 released
10	Sequences and series. Convergence Tests, Power series. Taylor and Maclaurin Series. Introduction to functions of two varibales (Domains, graphs and level curves),	Workshop C3; Assignment C3 released
11	Multivariable calculus-Limits, continuity and partial derivatives, Multivariable calculus-Tangent planes, Chain Rules, Implicit Differentiation. Gradient vectors and directional derivatives. Extrema and Optimisation, Double integrals.	Workshop C4; Assignment C4 released
12	Area Integrals, Double integrals in polar coordinates. Change of variables in double integrals.	Workshop C5; Assignment C5 released

Tutorial Registration

Log on to WATTLE to select your workshop class.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Linear Algebra Assignments	10 %	*	*	1,2,3,4
Mid-semester exam	38 %	30/08/2021	24/09/2021	1,2,3,4
Calculus Assignments	10 %	*	*	1,2,3,4
End-of-semester Exam	42 %	04/11/2021	02/12/2021	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 Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

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

Students are expected to contribute on an ongoing basis throughout the semester. To enable remote participation, lectures will be live-streamed and recorded, and at least one workshop per week will be offered as a zoom workshop.

Examination(s)

The due and return dates 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. To pass this class, it is a hurdle to have a weighted average of the two exams of 50%.

Assessment Task 1

Linear Algebra Assignments

In weeks 2, 3, 4, 5, 6 you will have a workshop on the linear algebra material in the course. Each workshop is accompanied by an assignment. Your assignment will become available in Wattle at 5 pm on the day of your workshop, and it will be due exactly 5 days after it becomes available. This cycle repeats for each of the five linear algebra workshops. Your Linear Algebra Assignments score will be determined by the average of your best four scores on individual linear algebra assignments.

Assessment Task 2

Mid-semester exam

There will be a mid-semester exam on all material from the linear algebra part of the course. The date range is a general indication of when the mid-semester exam will be held. The date of the exam will be determined by the Examinations Office.

Assessment Task 3

Calculus Assignments

In weeks 8, 9, 10, 11, 12 you will have a workshop on the calculus material in the course. Each workshop is accompanied by an assignment. Your assignment will become available in Wattle at 5 pm on the day of your workshop, and it will be due exactly 5 days after it becomes available. This cycle repeats for each of the five calculus workshops. Your Calculus Assignments score will be determined using the average of your best four scores on individual calculus assignments.

Assessment Task 4

End-of-semester Exam

There will be an end-of-semester exam on all material from the calculus part of the course. The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the course Wattle site and the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location exam.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to 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 be familiar with the academic integrity principle and Academic Misconduct Rule, 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 Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin or Wattle (check the Wattle page for more information). Further details can be found on the Course Wattle site.

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

Late submission is generally not permitted. See the Course Wattle website for further details and exceptions. Please note that we compute your assignment scores for each part of the course using only the best four of the five assignments.

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

It is intended that assignments will be graded within 7 days of submission. Assignment scores and feedback will be made available through Wattle.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted 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

No resubmission of 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