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.

Calculus topics to be covered include: 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 topics to be covered include: 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:

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

Examination Material or equipment

Please refer to information given on the course's Canvas site prior to exams, for details.

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:

Lay, David C., Steven R. Lay, and Judi J. McDonald. Linear Algebra and Its Applications, Global Edition. 5th ed. Rugby: Pearson Education, Limited, 2015.

You may access an e-version of this text for free through the ANU library.

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

I. Stewart, James. Essential Calculus. 2nd ed., Brooks/Cole, 2013. Several copies of this text are available for consultation in the Hancock Library.

II. Courant, R. and Robbins, H. What is Mathematics? ( https://en.wikipedia.org/wiki/What_Is_Mathematics%3F )

Recommended Resources

There are a variety of online platforms you will use to participate in your study program as a whole. These could include videos 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/or photo/scan for handwritten work and drawings, and home-based assessment.

ANU outlines recommended student system requirements to ensure you are able to participate fully in your learning. Other information is also available about the various Learning Platforms you may use.

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 groups, 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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Other Information

Please note that the timing of the class content is subject to variation.

Use of Artificial Intelligence (AI): invigilated assessment tasks prohibit the use of electronic devices, and no AI usage is allowed in such tasks. For other assessment tasks, the use of generative AI will be governed by the class policy as specified on Canvas or as part of the individual assessment task instructions.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Functions, Limits and the Squeeze Theorem, Continuity; Related rates and linear approximations. Derivatives, rates of change, and basic differentiation rules. Implicit differentiation.	No workshops in Week 1.
2	Minimum and Maximum values, Mean Value Theorem, Shape of graphs, L’Hospital’s Rule, Optimization Problems; Antiderivatives.	Workshop C1; Assignment C1 released
3	The definite integral, Evaluating Definite Integrals; Fundamental Theorem of Calculus; Inverse functions, logarithmic and exponential functions.	Workshop C2; Assignment C2 released
4	Integration techniques: by substitution and by parts; Trigonometric integrals and improper integrals; Exponential Growth and Decay; Differential equations.	Workshop C3; Assignment C3 released
5	Sequences and series. Convergence Tests, Power series. Taylor Series. Introduction to functions of two variables (Domains, graphs, and level curves); Multivariable calculus: continuity and partial derivatives.	Workshop C4; Assignment C4 released
6	Gradient vectors and directional derivatives. Extrema and Optimization, Double Integrals. Area Integrals, Double integrals in polar coordinates. Change of variables in double integrals.	Workshop C5; Assignment C5 released
7	Systems of linear equations [Lay 1.1]; The Row Reduction algorithm [Lay 1.2]; Vector operations [Lay 1.3].	No workshops in Week 7. The mid-semester exam is scheduled for Tuesday Week 7, in the 4pm to 6pm Assessment Activity slot in Melville Hall.
8	The matrix equation and solution sets of linear systems [Lay 1.4 and 1.5]; Linear independence [Lay 1.7]; Subspaces [Lay 2.8].	Workshop LA1; Assignment LA1
9	Subspaces and bases [Lay 2.9, 4.2 and 4.3]; Bases and coordinates [Lay 4.3, 4.4, and 4.5]; Matrix operations [Lay 2.1]	Workshop LA2; Assignment LA2
10	The inverse of a matrix [Lay 2.2 and 2.3]; Linear Transformations [Lay 1.8 and 1.9]; Determinants and their properties [Lay 3.1 and 3.2].	Workshop LA3; Assignment LA3
11	Using the determinant [Lay 3.3]; Eigenvalues, eigenvectors and the characteristic equation [Lay 5.1 and 5.2]; Diagonalization [Lay 5.3]; Complex numbers and complex eigenvalues [Lay A2 and 5.5].	Workshop LA4; Assignment LA4
12	Eigenvectors and linear transformations [Lay 5.3]; Applications of linear systems [Lay 1.6]; Applications to Markov Chains [Lay 4.9]; Revision.	Workshop LA5; Assignment LA5

Tutorial Registration

Workshops begin in Week 2. Registration is via MyTimetable. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities/tutorials so they can better plan their time. Find out more on the Timetable webpage.

Assessment Summary

Assessment task	Value	Due Date	Learning Outcomes
Calculus assignments	10 %	*	1,2,3,4
Mid-semester exam	40 %	22/09/2026	1,2,3,4
Linear Algebra Assignments	10 %	*	1,2,3,4
End-of-semester Exam	40 %	*	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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

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 Skills website. 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 ‘Canvas’ 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 actively participate on an ongoing basis throughout the semester. In-person workshop attendance is essential.

Examination(s)

Students should consult the course's Canvas site and the ANU final examination timetable to confirm the date, time, and venue of the exams.

Assessment Task 1

Calculus assignments

Five written assignments on the Calculus content. These are released in weeks 2, 3, 4, 5, 6 and are due four days after they are released. Your best four Calculus assignment scores will be used to determine this part of your grade. Please see Canvas and the individual assignment tasks for information about how they are to be graded.

Assessment Task 2

Mid-semester exam

There will be a mid-semester exam covering all material from the Calculus part of the course. It is scheduled for Tuesday of Week 7 (22 September, 2026), from 4:00 pm to 6:00 pm, in the Assessment Activity in Melville Hall (Building 12 on campus), as shown in MyTimetable. Further details will be provided on the course Canvas site.

Assessment Task 3

Linear Algebra Assignments

Five written assignments on the Linear Algebra content. These are released in weeks 8, 9, 10, 11, 12 and are due four days after they are released. Your best four Linear Algebra assignment scores will be used to determine this part of your grade. Please see Canvas and the individual assignment tasks for information about how they are to be graded.

Assessment Task 4

End-of-semester Exam

There will be an end-of-semester exam on all material from the Linear Algebra part of the course. It will be held during the official end-of-semester exam period. Please check the course's Canvas 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 of the exam.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

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. MATH1113 does not use Turnitin, having been granted an exemption. Further details about submission of assignments can be found on the Course's Canvas 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. Note that, for each part of the course, only the best 4 of 5 assignment scores contribute to the final grade.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material. Any use of artificial intelligence must be properly referenced. Failure to properly cite use of Generative AI will be considered a breach of academic integrity.

Returning Assignments

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

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 is permitted.

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 Accessibility 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 supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students