Students

MATH1015 – Calculus and Linear Algebra I (Advanced)

2026 – Session 1, In person-scheduled-weekday, North Ryde

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Unit convenor/Lecturer
Frank Valckenborgh
frank.valckenborgh@mq.edu.au
Contact via Email
12WW 613
Email me for an appointment.
Lecturer
Ji Li
ji.li@mq.edu.au
Contact via Email
12WW 710
Email me for an appointment.
Credit points Credit points
10
Prerequisites Prerequisites
(HSC Mathematics Extension 1 Band E3 and above or HSC Mathematics Extension 2) or admission to BActStud or BActStudProfPrac(Hons)
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description

This is the first mainstream university mathematics unit and is presented at a more advanced level than MATH1010. The material covered is essential for students studying mathematical or actuarial sciences. This subject provides an introduction to basic concepts and techniques in linear algebra and calculus. In algebra, topics covered include matrices, systems of linear equations and their applications, including the use of vectors in two and three-dimensional Euclidean geometry and linear optimisation. In calculus, the concept of a function of one variable is explored, and the notions of limit and continuity are developed. The concept of the derivative as a suitable construct to describe rates of change is defined and techniques of differential and integral calculus of functions of a real variable are developed. Some simple differential equations and their role as quantitative models for dynamic processes, are discussed. Students are also introduced to the use of computers in mathematics, and develop modelling and problem solving skills through theoretical and practical problems.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates

Learning Outcomes

On successful completion of this unit, you will be able to:

  • ULO1: Determine solutions to linear systems of equations using matrix tools and techniques.
  • ULO2: Employ techniques from linear algebra to analyse structures in 2- and 3-D Euclidean space, including vectors, lines and planes.
  • ULO3: Analyze a mathematical problem using concepts of limits, continuity and differentiability.
  • ULO4: Utilise the techniques of differentiation and integration with proficiency to a wide range of functions.
  • ULO5: Evaluate the context of a mathematical statement in order to determine the validity of a given argument, and to construct mathematical proofs.

General Assessment Information

Requirements to Pass this Unit

To pass this unit you must:

• Achieve a total mark equal to or greater than 50%.

Attendance and participation

We strongly encourage all students to actively participate in all learning activities. Regular engagement is crucial for your success in this unit, as these activities provide opportunities to deepen your understanding of the material, collaborate with peers, and receive valuable feedback from instructors, to assist in completing the unit assessments. Your active participation not only enhances your own learning experience but also contributes to a vibrant and dynamic learning environment for everyone.

Late Submission Policy

  • 5% penalty per day: If you submit your assessment late, 5% of the total possible marks will be deducted for each day (including weekends), up to 7 days. A 1-hour grace period will be provided to students who experience a technical concern.

    • Example 1 (out of 100): If you score 85/100 but submit 20 hours late, you will lose 5 marks and receive 80/100.

    • Example 2 (out of 30): If you score 27/30 but submit 1 day late, you will lose 1.5 marks and receive 25.5/30.

  • After 7 days: Submissions more than 7 days late will receive a mark of 0.

  • Extensions:

    • Automatic short extension: Some assessments are eligible for automatic short extension. You can only apply for an automatic short extension before the due date.

    • Special Consideration: If you need more time due to serious issues and for any assessments that are not eligible for Short Extension, you must apply for Special Consideration.

Need help? Review the Special Consideration page HERE.

Assessment Tasks

Name Weighting Hurdle Due Groupwork/Individual Short Extension AI assisted?
Assignment 20% No 29 May 2026, at 11:55pm Individual No Open AI
Final examination 50% No Final examination period Individual No Observed
Skills exercise 30% No Week 8 Individual No Observed

Assignment

Assessment Type 1: Problem-based task
Indicative Time on Task 2: 12 hours
Due: 29 May 2026, at 11:55pm
Weighting: 20%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Open

The assignment will test the ability of students to solve mathematical problems using concepts and techniques learnt in the unit.
On successful completion you will be able to:
  • Determine solutions to linear systems of equations using matrix tools and techniques.
  • Employ techniques from linear algebra to analyse structures in 2- and 3-D Euclidean space, including vectors, lines and planes.
  • Analyze a mathematical problem using concepts of limits, continuity and differentiability.
  • Utilise the techniques of differentiation and integration with proficiency to a wide range of functions.
  • Evaluate the context of a mathematical statement in order to determine the validity of a given argument, and to construct mathematical proofs.

Final examination

Assessment Type 1: Examination
Indicative Time on Task 2: 20 hours
Due: Final examination period
Weighting: 50%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Observed

The exam will test the ability of students to utilise concepts and techniques learnt in the unit.
On successful completion you will be able to:
  • Determine solutions to linear systems of equations using matrix tools and techniques.
  • Employ techniques from linear algebra to analyse structures in 2- and 3-D Euclidean space, including vectors, lines and planes.
  • Analyze a mathematical problem using concepts of limits, continuity and differentiability.
  • Utilise the techniques of differentiation and integration with proficiency to a wide range of functions.
  • Evaluate the context of a mathematical statement in order to determine the validity of a given argument, and to construct mathematical proofs.

Skills exercise

Assessment Type 1: Practice-based task
Indicative Time on Task 2: 18 hours
Due: Week 8
Weighting: 30%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Observed

Exercises designed to develop and assess mathematical skills, reinforcing theoretical knowledge through consistent practice to promote mastery of essential concepts.
On successful completion you will be able to:
  • Determine solutions to linear systems of equations using matrix tools and techniques.
  • Employ techniques from linear algebra to analyse structures in 2- and 3-D Euclidean space, including vectors, lines and planes.
  • Analyze a mathematical problem using concepts of limits, continuity and differentiability.
  • Utilise the techniques of differentiation and integration with proficiency to a wide range of functions.
  • Evaluate the context of a mathematical statement in order to determine the validity of a given argument, and to construct mathematical proofs.

1 If you need help with your assignment, please contact:

  • the academic teaching staff in your unit for guidance in understanding or completing this type of assessment
  • the Writing Centre for academic skills support.

2 Indicative time-on-task is an estimate of the time required for completion of the assessment task and is subject to individual variation.

3 An automatic short extension is available for some assessments. Apply through the Service Connect Portal.

Delivery and Resources

Classes

• Lectures (beginning in Week 1): There are two one-hour lectures each week.

• SGTA classes (beginning in Week 2) 

The timetable for classes can be found on the University website at: https://publish.mq.edu.au/.

Enrolment can be managed using eStudent at:

https://students.mq.edu.au/support/technology/systems/estudent

 

Course Notes: Student notes will be posted on iLearn.

Suggested textbooks:

The following textbooks are useful as supplementary resources, for additional questions and explanations. They are available from the Macquarie University library:

• Algebra - Lay, Linear Algebra and its Applications, 5th edition.

• Algebra - Axler, Linear Algebra Done Right, 4th edition.

• Calculus - Stewart, Calculus (Metric Version), 8th edition.

Methods of Communication

We will communicate with you via your university email or through announcements on iLearn. Queries to convenors can either be placed on the iLearn discussion board or sent to your lecturers from your university email address.

Unit Schedule

Planned Unit Schedule

Week Lecture 1 Lecture 2
1 Functions and limit Continuity
2 Derivatives and Implicit Differentiation Mean value theorem
3 Antiderivatives Indefinite Integration
4 Definite Integration Fundamental Theorem of Calculus
5 Substitution & Integration by Parts Differential Equations
6 First-Order Differential Equations Second-Order Differential Equations
7 Sets & Vectors Linear Systems
8 Matrices Vector Spaces
9 Gaussian Elimination Gaussian Elimination
10 Norms & Orthogonality Determinants
11 Determinant Properties Projection and Cross Products
12 Lines and Places Lines and Places
13 Revision (Linear Algebra) Revision (Calculus)

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://policies.mq.edu.au). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Students seeking more policy resources can visit Student Policies (https://students.mq.edu.au/support/study/policies). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

To find other policies relating to Teaching and Learning, visit Policy Central (https://policies.mq.edu.au) and use the search tool.

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/admin/other-resources/student-conduct

Results

Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit connect.mq.edu.au or if you are a Global MBA student contact globalmba.support@mq.edu.au

Academic Integrity

At Macquarie, we believe academic integrity – honesty, respect, trust, responsibility, fairness and courage – is at the core of learning, teaching and research. We recognise that meeting the expectations required to complete your assessments can be challenging. So, we offer you a range of resources and services to help you reach your potential, including free online writing and maths support, academic skills development and wellbeing consultations.

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

Academic Success

Academic Success provides resources to develop your English language proficiency, academic writing, and communication skills.

The Library provides online and face to face support to help you find and use relevant information resources. 

Student Services and Support

Macquarie University offers a range of Student Support Services including:

Student Enquiries

Got a question? Ask us via the Service Connect Portal, or contact Service Connect.

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/. 

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.

Changes from Previous Offering

We value student feedback to be able to continually improve the way we offer our units. As such we encourage students to provide constructive feedback via student surveys, to the teaching staff directly, or via the FSE Student Experience & Feedback link in the iLearn page.

Student feedback from the previous offering of this unit was very positive overall, with students pleased with the clarity around assessment requirements and the level of support from teaching staff. As such, no change to the delivery of the unit is planned, however we will continue to strive to improve the level of support and the level of student engagement.

Unit information based on version 2026.01R of the Handbook