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)

Staff Feedback

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

• written comments
• verbal comments
• feedback to 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.

Other Information

Please note, that where there are multiple assessment tasks of the same type, e.g weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. 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	Systems of linear equations; Gaussian elimination and row echelon forms; Applications of linear systems; Vectors and vector operations, Matrix-vector products.
2	Solution sets of linear systems; Linear independence; Subspaces and basis of a subspace; Dimension of subspaces
3	Inner products and orthogonality; Linear transformations, The matrix of a linear transformation; Matrix multiplication and other algebraic operations; Matrix inverses .
4	Characteristics of invertible matrices/invertible linear transformations; Determinants and their properties; Cramer's rule, determinant formula, and areas; Eigenvalues and eigenvectors.
5	Characteristic polynomial; Diagonalisation; Eigenvectors and linear transformations; Complex numbers.
6	Complex eigenvectors; Dynamical systems. Functions, limits and the Squeeze Theorem, Continuity; Related rates and linear approximations.
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;
8	Antiderivatives; Definite integral, Evaluating Definite Integrals; Fundamental Theorem of Calculus; Inverse functions, logarithmic and exponential functions.
9	Integration techniques: by substitutions and by parts; Trigonometric integrals and improper integrals. Integration for partial fractions, Exponential Growth and Decay. Differential equations.
10	Sequences and series. Convergence Tests, Power series. Taylor and Maclaurin Series. Introduction to functions of two varibales (Domains, graphs and level curves),
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.
12	Area Integrals, Double integrals in polar coordinates. Change of variables in double integrals.

Tutorial Registration

Log on to WATTLE to select your workshop class.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignments	20 %	03/08/2020	02/11/2020	1,2,3,4
Online Quizzes	10 %	03/08/2020	02/11/2020	1,2,3,4
Mid semester exam	32 %	31/08/2020	25/09/2020	1,2,3,4
End of Semester Exam	38 %	05/11/2020	03/12/2020	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 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 on-going basis throughout the semester.

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

Assignments

There will be 8 assignments during the semester. These may be longer assignment to be completed within seven days, or shorter assignment to be completed in a fixed amount of time at a given time (for instance during the workshops). Further details can be found on the Course Wattle site.

Assessment Task 2

Online Quizzes

There will be 10 online quizzes on WebAssign. Students should receive an introductory email from the WebAssign system during the first week. The weight of the quizzes will be worth 10%. Further details can be found on the Course Wattle site.

Assessment Task 3

Mid semester exam

There will be a mid-semester exam on all material from the linear algebra part, covered in the first six weeks. The date range is a general indication of when the mid-semester exam will be held.

Assessment Task 4

End of Semester Exam

There will be a mid-semester exam on all material from the calculus part, covered in weeks 7-12. 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.

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

Assignments will be marked by demonstrators online so students can view any feedbacks. 

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