Students

MATH1025 – Calculus and Linear Algebra II (Advanced)

2024 – Session 2, In person-scheduled-weekday, North Ryde

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff
Stuart Hawkins
stuart.hawkins@mq.edu.au
Xuan Duong
xuan.duong@mq.edu.au
Credit points Credit points
10
Prerequisites Prerequisites
MATH1010(HD) or MATH1015 or MATH135(HD) or MATH132
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%, and
  • Participate in, and undertake all the Practice-based activities for a minimum of 10 of the 12 weekly SGTAs.

Hurdle Assessments

Practice-based skills for SGTA classes (0%)

Development of knowledge and skills requires continual practice. During SGTAs you will practice a range of mathematical techniques. To pass this hurdle assessment, you must be able to demonstrate your progress in developing and communicating knowledge and skills in 10 of the 12 SGTAs. This is a hurdle assessment meaning that failure to meet this requirement may result in a fail grade for the unit. Students are permitted up to two absences: additional absences will require a Special Consideration to be applied for (see below).

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 scheduled tests/exams, performance assessments/presentations, and/or scheduled practical assessments/labs, please apply for Special Consideration.

Assessments where Late Submissions will be accepted:

  • Assignment – YES, Standard Late Penalty applies
  • Major Tests 1 and 2 - NO, unless Special Consideration is Granted
  • Weekly quizzes - 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 ask.mq.edu.au.

Written Assessments/Quizzes/Tests: 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 ask.mq.edu.au.

Weekly practice-based tasks for SGTA classes: To pass the unit you need to demonstrate ongoing development of skills and application of knowledge in 10 out of 12 of the weekly SGTA classes. If you miss a weekly SGTA class due to a serious, unavoidable and significant disruption, contact your convenor ASAP as you may be able to attend another class that week. If it is not possible to attend another class, you should still contact your convenor for access to class material to review in your own time. Note that a Special Consideration should only be applied for if you miss more than two of the weekly practical classes.

Assessment Tasks

Name Weighting Hurdle Due
Weekly Quiz 16% No Weeks 2, 3, 4, 6, 7, 8, 9, 10 and 12
Major Test 1 12% No Week 5
Major Test 2 12% No Week 11
Assignment 10% No Week 12
Participation in SGTA classess 0% Yes Weeks 2 to 13
Final Examination 50% No Exam period

Weekly Quiz

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 9 hours
Due: Weeks 2, 3, 4, 6, 7, 8, 9, 10 and 12
Weighting: 16%

 

The subject will have nine weekly online (iLearn) quizzes containing one to three short questions. The quizzes will last for one hour, and be available for a duration of one week. The quizzes will not run in Week 1, or weeks containing a midterm test. Each quiz is worth 2%, with the best eight quizzes counted to the overall grade.

 
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.

Major Test 1

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 7 hours
Due: Week 5
Weighting: 12%

 

This will be an online test held during the semester. It will test the ability of students to analyse and solve mathematical problems using concepts and techniques in linear algebra and calculus.

 
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.

Major Test 2

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 7 hours
Due: Week 11
Weighting: 12%

 

This will be an online test held during the semester. It will test the ability of students to analyse and solve mathematical problems using concepts and techniques in linear algebra and calculus.

 
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.

Assignment

Assessment Type 1: Problem set
Indicative Time on Task 2: 7 hours
Due: Week 12
Weighting: 10%

 

This assignment will test the ability of students to solve theoretical mathematical problems using concepts and techniques from linear algebra and calculus, and prove mathematical statements.

 
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.

Participation in SGTA classess

Assessment Type 1: Practice-based task
Indicative Time on Task 2: 0 hours
Due: Weeks 2 to 13
Weighting: 0%
This is a hurdle assessment task (see assessment policy for more information on hurdle assessment tasks)

 

Development of knowledge and skills requires continual practice. During SGTAs you will practice a range of mathematical techniques. To pass this hurdle assessment, you must be able to demonstrate your progress in developing and communicating knowledge and skills in 10 out of 12 SGTAs.

 
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: 15 hours
Due: Exam period
Weighting: 50%

 

This will be held during the final exam period. It will test the ability of students to synthesise the concepts taught in the course in order to analyse and solve mathematical problems with various applications.

 
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): Students must register in and attend one one-hour class per week. This is a hurdle requirement. Missing more than two SGTA classes will result in failure of the unit.

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

Week Topic Assessment

1

Vectors, linear combinations, elementary matrices.

  

2

Inverse matrices, LU decomposition, determinants.

  

3

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

  

4

Bases and dimension, eigenvalues and eigenvectors.

  

5

Eigenspaces and diagonalisation, powers of matrices, linear transformations.

Test 1

6

Matrix of a linear transformation, composition of linear transformations.

  

7

Limits, improper integrals, indeterminate forms, continuity.

  

8

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

  

9

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

  

10

Polynomials, Taylor polynomials, infinite series.

  

11

Functions of several variables, partial derivatives.

Test 2

12

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

Assignment

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/

The Writing Centre

The Writing Centre 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 2024.01R of the Handbook