Students

MATH1025 – Calculus and Linear Algebra II (Advanced)

2025 – Session 2, In person-scheduled-weekday, North Ryde

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff
Xuan Duong
xuan.duong@mq.edu.au
Contact via xuan.duong@mq.edu.au
12 Wally's Walk, Room 729
Noa Kraitzman
noa.kraitzman@mq.edu.au
Contact via noa.kraitzman@mq.edu.au
12 Wally's Walk, Room 739
Credit points Credit points
10
Prerequisites Prerequisites
MATH1010(HD) or MATH1015
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description

The foundations of linear algebra and calculus introduced in MATH1015 are further explored and extended. Topics covered in algebra include: inverse matrices, determinants, vector spaces & subspaces, eigenvalues and eigenvectors and linear transformations. In calculus the topics include: the further development of the concepts of limits, continuity and the derivative, numerical integration, polynomials, sequences & series and differential equations. In addition, complex numbers and the calculus of two or more variables are introduced. Students utilise mathematical software throughout the course to support and enhance problem solving for a variety of 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: Apply matrix inversion and decomposition methods to determine solutions to systems of linear equations.
  • ULO2: Analyse vectors and linear maps in spaces of arbitrary dimension, developing concepts such as vector spaces and eigenspaces.
  • ULO3: Utilise complex numbers and techniques of differentiation and integration to determine and compare properties of single variable and multivariable functions.
  • ULO4: Analyse the convergence of a wide range of infinite series, including Taylor series.
  • ULO5: Evaluate elementary numerical techniques for root finding, function approximation and integration, in order to assess the convergence criteria or the error estimate of the method.

General Assessment Information

Requirements to Pass this Unit

To pass this unit you must:

  • Achieve a total mark equal to or greater than 50% across all assessments

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 partici- pation not only enhances your own learning experience but also contributes to a vibrant and dynamic learning environment for everyone.

Late Assessment Submission Penalty

Unless a Special Consideration request has been submitted and approved, a 5% penalty (of the total possible mark of the task) will be applied for each day a written report or presentation assessment is not submitted, up until the 7th day (including weekends). After the 7th day, a grade of ‘0’ will be awarded even if the assessment is submitted. The submission time for all uploaded assessments is 11:55 pm. A 1-hour grace period will be provided to students who experience a technical concern.

For any late submission of time-sensitive tasks, such as assignment/skills exercise/exam, please apply for Special Consideration.

Assessments where Late Submissions will be accepted:

  • Assignment: YES, Standard Late Penalty applies, unless Special Consideration is Granted
  • Skills Exercise: NO, unless Special Consideration is Granted

Special Consideration

The Special Consideration Policy aims to support students who have been impacted by short-term circumstances or events that are serious, unavoidable and significantly disruptive, and which may affect their performance in assessment. If you experience circumstances or events that affect your ability to complete the assessments in this unit on time, please inform the convenor and submit a Special Consideration request through https://connect.mq.edu.au.

Assignments/Skills Exercise: If you experience circumstances or events that affect your ability to complete the written assessments in this unit on time, please inform the convenor and submit a Special Consideration request through https://connect.mq.edu.au.

Assessment Tasks

Name Weighting Hurdle Due
Assignment 20% No 11:55 pm 31st Oct 2025
Skills exercise 30% No 11:55 pm 07th Nov 2025
Final examination 50% No Exam period

Assignment

Assessment Type 1: Problem set
Indicative Time on Task 2: 12 hours
Due: 11:55 pm 31st Oct 2025
Weighting: 20%

 

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:
  • Apply matrix inversion and decomposition methods to determine solutions to systems of linear equations.
  • Analyse vectors and linear maps in spaces of arbitrary dimension, developing concepts such as vector spaces and eigenspaces.
  • Utilise complex numbers and techniques of differentiation and integration to determine and compare properties of single variable and multivariable functions.
  • Analyse the convergence of a wide range of infinite series, including Taylor series.
  • Evaluate elementary numerical techniques for root finding, function approximation and integration, in order to assess the convergence criteria or the error estimate of the method.

Skills exercise

Assessment Type 1: Practice-based task
Indicative Time on Task 2: 18 hours
Due: 11:55 pm 07th Nov 2025
Weighting: 30%

 

Students will complete a series of exercises designed to develop and assess their mathematical skills, reinforcing theoretical knowledge through consistent practice to promote mastery of essential concepts. These exercises will be submitted together for grading at one specific time. 

 
On successful completion you will be able to:
  • Apply matrix inversion and decomposition methods to determine solutions to systems of linear equations.
  • Analyse vectors and linear maps in spaces of arbitrary dimension, developing concepts such as vector spaces and eigenspaces.
  • Utilise complex numbers and techniques of differentiation and integration to determine and compare properties of single variable and multivariable functions.
  • Analyse the convergence of a wide range of infinite series, including Taylor series.
  • Evaluate elementary numerical techniques for root finding, function approximation and integration, in order to assess the convergence criteria or the error estimate of the method.

Final examination

Assessment Type 1: Examination
Indicative Time on Task 2: 20 hours
Due: Exam period
Weighting: 50%

 

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:
  • Apply matrix inversion and decomposition methods to determine solutions to systems of linear equations.
  • Analyse vectors and linear maps in spaces of arbitrary dimension, developing concepts such as vector spaces and eigenspaces.
  • Utilise complex numbers and techniques of differentiation and integration to determine and compare properties of single variable and multivariable functions.
  • Analyse the convergence of a wide range of infinite series, including Taylor series.
  • Evaluate elementary numerical techniques for root finding, function approximation and integration, in order to assess the convergence criteria or the error estimate of the method.

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

Delivery and Resources

Classes

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

SGTA classes (beginning in Week 2): There is one one-hour class per week. 

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.

Methods of Communication

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

Unit Schedule

1

Limits, improper integrals, indeterminate forms, continuity.

  

2

Intermediate value theorem, Newton's Method, Rolle's Theorem, Mean Value Theorem, numerical integration, complex numbers.

  

3

Argand plane, polar form, De Moivre's Theorem, polynomials

  

4

Polynomials, Taylor polynomials, infinite series.

  

5

Functions of several variables, partial derivatives.

   

6

Directional derivatives, extrema, second order ODEs, systems of ODEs.

7

Vectors, linear combinations, elementary matrices.                                                                                                                     

  

8

Inverse matrices, LU decomposition, determinants.

  

9

Determinants, adjugates, linear dependence, vector spaces and subspaces.

  

10

Bases and dimension, eigenvalues and eigenvectors.

  

11    

Eigenspaces and diagonalisation, powers of matrices, linear transformations      

     

12

Directional derivatives, extrema, second order ODEs, systems of ODEs.                                                                        .

Assignment

13

    Revision                                                                                                                                                                    .

Skills Exercise

 

 

 

 

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

To enable students more time to focus on learning, understanding and reflecting on the content of our unit we have revised the assessment structure as follows. There are now only three assessments: a skills assessment, an assignment and final exam. Although no marks are associated with attendance, all activities provide you with key content designed to help you understand content and complete the assessments.

Unit information based on version 2025.04 of the Handbook