Students

MATH2010 – Calculus and Linear Algebra III

2021 – Session 2, Special circumstances

Session 2 Learning and Teaching Update

The decision has been made to conduct study online for the remainder of Session 2 for all units WITHOUT mandatory on-campus learning activities. Exams for Session 2 will also be online where possible to do so.

This is due to the extension of the lockdown orders and to provide certainty around arrangements for the remainder of Session 2. We hope to return to campus beyond Session 2 as soon as it is safe and appropriate to do so.

Some classes/teaching activities cannot be moved online and must be taught on campus. You should already know if you are in one of these classes/teaching activities and your unit convenor will provide you with more information via iLearn. If you want to confirm, see the list of units with mandatory on-campus classes/teaching activities.

Visit the MQ COVID-19 information page for more detail.

General Information

Download as PDF
Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor/Lecturer
Adam Sikora
Contact via Email
Room: 721 WW12
Please refer to iLearn
Unit Convenor/Lecturer
Elena Vynogradova
Contact via Email
Room 709 WW12
Please refer to iLearn
Frank Schoenig
Credit points Credit points
10
Prerequisites Prerequisites
MATH1020 or MATH1025 or MATH133 or MATH136 or WMAT1020 or WMAT136
Corequisites Corequisites
Co-badged status Co-badged status
MATH2055
Unit description Unit description

The idea of a vector space first introduced in MATH1020 and MATH1025 is enriched in this unit by the introduction of an inner product. This leads to the important notion of orthogonality that underpins many areas of mathematics. The idea of linear transformations which transfer linearity from one space to another is also discussed. The results and techniques are then applied to problems such as approximation, quadratic forms and Fourier series. Differential and integral calculus involving functions of two real variables introduced in MATH1020 and MATH1025 are generalised to multivariable calculus including vector-valued functions, multivariable Taylor approximations, constrained optimization and multiple integrals in various coordinate systems. The ideas introduced in the unit are central to the development of many areas of modern areas of mathematics and to mathematical modelling of real world phenomena encounter in scientific and engineering problems.

Important Academic Dates

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

Learning Outcomes

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

  • ULO1: Determine the rates of change of systems that vary over space and time and construct approximate representations for them (multi-variable Taylor series).
  • ULO2: Formulate and solve simple physical problems through the use of linear techniques.
  • ULO3: Develop multiple representations for a system and justify the best choice physically (eg. Fourier Series).
  • ULO4: Successfully communicate how the mathematical methods developed in the unit relate to real world systems.

General Assessment Information

HURDLES: Attendance at, and reasonable engagement in, Small Group Teaching Activities (SGTA) classes in all first year mathematics and statistics units is compulsory. Attendance and reasonable engagement in the class activities in at least 10 out of 12 of the SGTA classes are requirements to pass the unit. This is a hurdle requirement.

ATTENDANCE and PARTICIPATION: Please contact the unit convenor as soon as possible if you have difficulty attending and participating in any classes. There may be alternatives available to make up the work. If there are circumstances that mean you will miss a class, you can apply for Special Consideration via ask.mq.edu.au

ASSIGNMENT SUBMISSION: Assignment submission will be online through the iLearn page.

Submit assignments online via the appropriate assignment link on the iLearn page. A personalised cover sheet is not required with online submissions. Read the submission statement carefully before accepting it as there are substantial penalties for making a false declaration.

  • Assignment submission is via iLearn. You should upload this as a single scanned PDF file.
  • Please note the quick guide on how to upload your assignments provided on the iLearn page.
  • Please make sure that each page in your uploaded assignment corresponds to only one A4 page (do not upload an A3 page worth of content as an A4 page in landscape). If you are using an app like Clear Scanner, please make sure that the photos you are using are clear and shadow-free.
  • It is your responsibility to make sure your assignment submission is legible.
  • If there are technical obstructions to your submitting online, please email us to let us know.

You may submit as often as required prior to the due date/time. Please note that each submission will completely replace any previous submissions. It is in your interests to make frequent submissions of your partially completed work as insurance against technical or other problems near the submission deadline.

LATE SUBMISSION OF WORK:  All assessment tasks must be submitted by the official due date and time. In the case of a late submission for a non-timed assessment (for example, an assignment), if special consideration has NOT been granted, 20% of the earned mark will be deducted for each 24-hour period (or part thereof) that the submission is late for the first 2 days (including weekends and/or public holidays). For example, if an assignment is submitted 25 hours late, its mark will attract a penalty equal to 40% of the earned mark. After 2 days (including weekends and public holidays) a mark of 0% will be awarded. Timed assessment tasks (for example, tests and examinations) do not fall under these rules.

FINAL EXAM POLICY: It is Macquarie University policy not to set early examinations for individuals or groups of students. All students are expected to ensure that they are available until the end of the teaching semester, that is, the final day of the official examination period. The only excuse for not sitting an examination at the designated time is because of documented illness or unavoidable disruption. In these special circumstances, you may apply for special consideration via ask.mq.edu.au.

If you receive special consideration for the final exam, a supplementary exam will be scheduled in the interval between the regular exam period and the start of the next session. By making a special consideration application for the final exam you are declaring yourself available for a resit during this supplementary examination period and will not be eligible for a second special consideration approval based on pre-existing commitments. Please ensure you are familiar with the policy prior to submitting an application.

You can check the supplementary exam information page on FSE101 in iLearn (bit.ly/FSESupp) for dates, and approved applicants will receive an individual notification one week prior to the exam with the exact date and time of their supplementary examination.

Assessment Tasks

Name Weighting Hurdle Due
SGTA Participation 0% Yes Weekly (from Week 2)
Major Test 1 (online) 15% No Week 6
Major Test 2 (online) 15% No Week 11
Assignment 20% No Week 12
Final exam 50% No University Examination Period

SGTA Participation

Assessment Type 1: Participatory task
Indicative Time on Task 2: 0 hours
Due: Weekly (from Week 2)
Weighting: 0%
This is a hurdle assessment task (see assessment policy for more information on hurdle assessment tasks)

 

Students are expected to demonstrate their ability to engage with the unit by actively participating in SGTA classes.

 


On successful completion you will be able to:
  • Determine the rates of change of systems that vary over space and time and construct approximate representations for them (multi-variable Taylor series).
  • Formulate and solve simple physical problems through the use of linear techniques.
  • Develop multiple representations for a system and justify the best choice physically (eg. Fourier Series).
  • Successfully communicate how the mathematical methods developed in the unit relate to real world systems.

Major Test 1 (online)

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 7 hours
Due: Week 6
Weighting: 15%

 

Online test

 


On successful completion you will be able to:
  • Determine the rates of change of systems that vary over space and time and construct approximate representations for them (multi-variable Taylor series).
  • Formulate and solve simple physical problems through the use of linear techniques.
  • Develop multiple representations for a system and justify the best choice physically (eg. Fourier Series).
  • Successfully communicate how the mathematical methods developed in the unit relate to real world systems.

Major Test 2 (online)

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 7 hours
Due: Week 11
Weighting: 15%

 

Online test

 


On successful completion you will be able to:
  • Determine the rates of change of systems that vary over space and time and construct approximate representations for them (multi-variable Taylor series).
  • Formulate and solve simple physical problems through the use of linear techniques.
  • Develop multiple representations for a system and justify the best choice physically (eg. Fourier Series).
  • Successfully communicate how the mathematical methods developed in the unit relate to real world systems.

Assignment

Assessment Type 1: Problem set
Indicative Time on Task 2: 7 hours
Due: Week 12
Weighting: 20%

 

One assignment submitted electronically

 


On successful completion you will be able to:
  • Determine the rates of change of systems that vary over space and time and construct approximate representations for them (multi-variable Taylor series).
  • Formulate and solve simple physical problems through the use of linear techniques.
  • Develop multiple representations for a system and justify the best choice physically (eg. Fourier Series).
  • Successfully communicate how the mathematical methods developed in the unit relate to real world systems.

Final exam

Assessment Type 1: Examination
Indicative Time on Task 2: 12 hours
Due: University Examination Period
Weighting: 50%

 

This will be an invigilated exam, 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:
  • Determine the rates of change of systems that vary over space and time and construct approximate representations for them (multi-variable Taylor series).
  • Formulate and solve simple physical problems through the use of linear techniques.
  • Develop multiple representations for a system and justify the best choice physically (eg. Fourier Series).
  • Successfully communicate how the mathematical methods developed in the unit relate to real world systems.

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 Learning Skills Unit 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:  There are 2 one-hr online lectures each week and 1 SGTA class each week. Students are strongly encouraged to attend both lectures each week.

SGTA: You should attend and participate in one Small Group Teaching Activity (SGTA) each week, from Week 2.  Students must participate in the SGTA in which they are enrolled. Any variation to this has to be approved by the convenor. This is a hurdle requirement.

This unit will use: iLearn; students need regular access to a reliable internet connection. MATLAB; students need regular access to the computer program MATLAB (available for download onto personally owned devices, and on computers around campus).

Textbooks:

  • Anton & Rorres: Elementary Linear Algebra, Applications Version , 11th Edition, Wiley 2014
  • Stewart, Calculus (Metric Version), 8th edition.

Unit Schedule

Week

Topic

Assessment Due
  Stream 1 - Calculus  

1

Euclidean spaces; Functions of many variable;. Graphs of functions; Lines, planes and hyperplanes.

 

2

Limits and continuity in one, two and higher dimensions; Arithmetic of limits; Polar coordinates.

 

3

Partial derivative;. Directional derivatives and the gradient; Implicit differentiation and implicit function theorem; Vector-valued functions.

 

4

Multivariate differentiability; Arithmetic of differentiable functions; The chain rule.

 

5

Second order partial derivatives; First and second order Taylor approximations; Local extrema; Constrained optimisation.

 

6

Multiple integrals; Change of variable for multiple integrals; Inverse function theorem.

Test 1
  Stream 2 - Algebra  

7

Linear Systems, Vector spaces, Basis and dimension;

 

8

Change of basis; Linear transformations; matrices for linear transformations.

 

9

Range and kernel of linear transformation; Column space (or range) of a matrix; Eigenvalues and eigenspaces of linear transformations;  Matrices of linear transformations in different bases.

 

10

Similar matrices; Diagonalisation; Inner product; Norms; Orthogonality; Fourier Series.

 

11

Gram-Schmidt process; Orthogonal matrices; Symmetric matrices; Quadratic forms.

Test 2

12

Orthogonal projections; Least squares approximations; Complex vector spaces.

Assignment 
  Note: this schedule is provisional and may vary from the delivered content  

 

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central). Students should be aware of the following policies in particular with regard to Learning and Teaching:

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

If you would like to see all the policies relevant to Learning and Teaching visit Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central).

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 ask.mq.edu.au or if you are a Global MBA student contact globalmba.support@mq.edu.au

Student Support

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

Learning Skills

Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to help you improve your marks and take control of your study.

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

Student Enquiry Service

For all student enquiries, visit Student Connect at ask.mq.edu.au

If you are a Global MBA student contact globalmba.support@mq.edu.au

Equity Support

Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.

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.