School of Engineering and Computer Science Te Kura Mātai Pūkaha, Pūrorohiko

ENGR222 (2024) - Computational Algebra and Calculus

Prescription

This course covers fundamental concepts in linear algebra and multivariable calculus, with an emphasis on their applications to physical and engineering problems. Topics covered include linear transformations, matrix decomposition including the singular value decomposition, Taylor series, calculus of vector-valued functions, multivariate functions and vector fields. Mathematical software will be used extensively.

Course learning objectives

Students who pass this course should be able to:

  1. State the definitions of fundamental concepts in linear algebra and multivariable calculus.
  2. Demonstrate ways in which linear algebra and multivariable calculus can be used to model physical and engineering problems.
  3. Apply concepts and techniques in linear algebra and multivariable calculus to solve physical and engineering problems, both manually and using software tools when appropriate.

Course content

We’ve designed this course for in-person study, and to get the most of out it we strongly recommend you attend lectures on campus. Most assessment items, as well as tutorials/seminars/labs/workshops will only be available in person. Any exceptions for in-person attendance for assessment will be looked at on a case-by-case basis in exceptional circumstances, e.g., through disability services or by approval by the course coordinator.

Withdrawal from Course

Withdrawal dates and process:
https://www.wgtn.ac.nz/students/study/course-additions-withdrawals

Lecturers

Dr Brendan Harding (Coordinator)

Emma Greenbank

Teaching Format

There will be 3 lectures each teaching week. Additionally, there'll be a computer lab most weeks starting in week 2. Attendance in person is strongly encouraged. Lectures will be used to introduce fundamental concepts along with techniques for modelling and solving problems. The computer labs will be used to teach software tools that can implement mathematical models and visualise problems, as well as compute solutions to them.

Dates (trimester, teaching & break dates)

  • Teaching: 26 February 2024 - 31 May 2024
  • Break: 01 April 2024 - 14 April 2024
  • Study period: 03 June 2024 - 06 June 2024
  • Exam period: 07 June 2024 - 22 June 2024

Class Times and Room Numbers

26 February 2024 - 24 March 2024

  • Friday 14:10 - 15:00 – LT103, Hugh Mackenzie, Kelburn

26 February 2024 - 31 March 2024

  • Monday 14:10 - 15:00 – LT103, Hugh Mackenzie, Kelburn

  • Wednesday 14:10 - 15:00 – LT103, Hugh Mackenzie, Kelburn

15 April 2024 - 02 June 2024

  • Monday 14:10 - 15:00 – LT103, Hugh Mackenzie, Kelburn

  • Wednesday 14:10 - 15:00 – LT103, Hugh Mackenzie, Kelburn

  • Friday 14:10 - 15:00 – LT103, Hugh Mackenzie, Kelburn

Other Classes

Computer labs will start in Week 2.

Required

There are no required texts for this offering.

  • "Engineering mathematics : a foundation for electronic, electrical, communications and systems engineers" (5th edition) by Anthony Croft and Robert Davison is a useful support book for this course, though it does not cover all the content and also includes material from 100-level and otherwise not in this course. Lecture notes will be provided.

Mandatory Course Requirements

There are no mandatory course requirements for this course.

If you believe that exceptional circumstances may prevent you from meeting the mandatory course requirements, contact the Course Coordinator for advice as soon as possible.

Assessment

For engineering, mathematics provides an incredibly powerful set of tools and techniques for representing physical situations - these are mathematical models - and using them to explain and make predictions about the world and our observations of it. When we learn mathematics, we aim to understand how these models work, and how they build on what we already know. To help us build our undestanding, we try to solve mathematical problems. This involves accurate calculation, knowing and understanding the rules of mathematical manipulation, following logical arguments, clearly explaining our mathematical reasoning both for ourselves and others, and seeing how abstraction can create analogies between different situations and models.
 
To test how well our understanding is developing, we need to attempt to apply techniques and solve problems regularly. In this and in most mathematics courses, we set regular assignments to help do this. They are intended to prompt you to undertstand what you have been learning in classes and through reading, so they are part of your learning process. But they take time and effort and so we want to encourage and reward you for this. So, while assignments are part of your learning, we also make them part of the assessment.
 
Engineers also want to make sure their calculations are accurate and computers help greatly with this. Many mathematical techniques are computational and can be carried out by computer programmes. So another part of this course is learning one programming language that is helpful for mathematics and data analysis, namely Python. We will assess your ability to use Python as a computational tool through weekly computer laboratories.
 
Finally, mathematical ideas and connections between them take time to form in our minds. So we also want to assess your learning when this has had time to take place. The two tests that form part of the assessment enable you to demonstrate your mathematical knowledge and abilities in this cumulative way.

Assessment ItemDue Date or Test DateCLO(s)Percentage
6 assignments, each requiring approximately 10 hrs workdue in weeks 2,4,6,8,10,12CLO: 2,320%
Notebooks for 5 computer laboratories3,5,7,9,11CLO: 2,320%
Test (2 hour duration)Week 6 or 7CLO: 1,2,330%
Test (2 hour duration)Assessment periodCLO: 1,2,330%

Penalties

Late assignments are not marked. Extensions may be granted in exceptional circumstances but must be sought before the deadline.

Extensions

Extensions must be asked for before the due date, and will be treated on a case by case basis by the lecturer. Always include a description of what you have completed so far and how much more time you think you will need. A different assessment is due most weeks so extensions will normally be granted for no more than three days.

Submission & Return

Assessments are to be submitted using Nuku and feedback on marked work will be provided via Nuku.
 
Student submitted work may be used during the formal Engineering NZ re-accreditation visit to VUW scheduled for 2024, as part of the evaluation process for the programme.

Marking Criteria

When you are writing out solutions to problems in mathematics, you will need to use quite a lot of symbolic notation. It is important to learn how to use this correctly. It is also important to explain your answers so that someone else can clearly follow your reasoning. So as well as using equations and formulas, you will also need to use ordinary language to clarify your thinking for the assessors. See how this is done in examples and worked solutions so you can see what is expected.
 
Marks will be given for correct working and use of correct methods, for clear logical explanations, correct use of notation and, where helpful, for diagrams and graphs. In programming exercises, correct use of syntax and explanatory comments will gain maximum marks. Where possible, we will give credit for correct working even where it is based on an earlier mistake, so long as that does not significantly simplify the problem.

Workload

The total workload for this course is 150 hours.

Teaching Plan

Communication of Additional Information

Information will be communicated to students by posting it on Nuku.

Offering CRN: 33042

Points: 15
Prerequisites: (ENGR 121, 122) or (MATH 142, 151)
Duration: 26 February 2024 - 23 June 2024
Starts: Trimester 1
Campus: Kelburn

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