ENGR121 (2023) - Engineering Mathematics Foundations


An introduction to the range of mathematical techniques employed by engineers, including functions, calculus, linear algebra, vector geometry, set theory, logic and probability. There is an emphasis on applications and modelling.

Course learning objectives

Students who pass this course should be able to:

  1. Read, interpret and manipulate mathematical expressions and equations in a variety of contexts.
  2. Apply mathematical concepts and techniques to analyse engineering systems and solve engineering problems.
  3. Demonstrate mastery of a range of fundamental mathematical techniques.
  4. Creatively and collaboratively combine skills and knowledge from mathematics, physics, computing and engineering to model an engineering problem.

Course content

This course is designed for in-person study, and it is strongly recommended that students attend lectures and tutorials on campus. In particular some assessment items will have a requirement of in-person attendance, although exceptions can be made under special circumstances.
Queries about any such exceptions can be sent to remote-enrolments@sms.vuw.ac.nz.
Topics covered in this course include: sets, number, functions, logic, algebraic techniques, trig functions, sequences, series, limits, differentiation, integration, vectors, matrix algebra and probability.

Required Academic Background

In 2021-2022, 12 credits of NCEA Level 3 in Mathematics/Statistics (or equivalent) will be accepted for entry, due to disruptions to teaching, learning and assessment caused by COVID-19.

Withdrawal from Course

Withdrawal dates and process:


Dr Tanya Gvozdeva (Coordinator)

Dr Ghassem Narimani

Dr Howard Lukefahr

Dr Steven Archer

Teaching Format

Four lectures, one tutorial, and one two-hour lab most weeks. Lectures are recorded to video and available to students through Nuku.

Student feedback

Feedback from previous students is available at http://www.cad.vuw.ac.nz/feedback/feedback_display.php

Dates (trimester, teaching & break dates)

  • Teaching: 27 February 2023 - 02 June 2023
  • Break: 10 April 2023 - 23 April 2023
  • Study period: 05 June 2023 - 08 June 2023
  • Exam period: 09 June 2023 - 24 June 2023

Class Times and Room Numbers

27 February 2023 - 02 April 2023

  • Friday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn
27 February 2023 - 09 April 2023

  • Monday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn
  • Tuesday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn
  • Thursday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn
24 April 2023 - 04 June 2023

  • Monday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn
  • Tuesday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn
  • Thursday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn
  • Friday 09:00 - 09:50 – LT205, Hugh Mackenzie, Kelburn

Other Classes

A two-hour lab each week, for eight of the weeks available.
One hour tutorial each week


There is no set text for this course. Detailed typeset lecture notes are made available online in the Home Pages.

There is no set text for this course, but we follow Croft et al, the recommended text, very closely. It is also the text for ENGR 122, and can be purchased from Vic Books. Stroud's book is also recommended if students want to read further.

  • Engineering Mathematics: a Foundation for Electronic, Electrical, Communications and Systems Engineers, 4th edition or later, by Anthony Croft, Robert Davison, Martin Hargreaves and James Flint, Pearson, 2012 or later.
  • Engineering Mathematics, by K.A. Stroud, with Dexter J. Booth. Palgrave MacMillan, London.

Mandatory Course Requirements

In addition to achieving an overall pass mark of at least 50%, students must:

  • Score at least 30% in the final test.

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.


This course is assessed through a combination of assignments, tests and lab reports. In order to gain maximum marks, it is highly recommended students attempt all assessments.
This assessment information is subject to change for 2023.

Assessment ItemDue Date or Test DateCLO(s)Percentage
AssignmentsMost WeeksCLO: 1,2,3,420%
Lab ReportsSee websiteCLO: 1,2,3,420%
TestSee websiteCLO: 1,2,3,419%
Final testSee websiteCLO: 1,2,3,440%
Diagnostic quizsee websiteCLO: 1,2,3,41%


Late assignments will not be marked. You can miss up to two (out of eight) assignments without losing any credit.
Late lab reports will result in lost marks, 10% loss for each day up to five days late. Later reports will not be marked.
Any plagiarism is likely to result in zero marks for both parties.


Extensions are not given for assignments or labs. Late assignments will not be marked. Lab reports that are more than five days late are not marked.

Submission & Return

All lab reports and assignments are submitted through the ECS online system, accessed through the ENGR 121 home pages.
Lab asssignment and test results are posted on the ECS online system. Feedback on lab reports and assignments are provided through the course Home page.
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

All assignments have the same value and will be marked fully. You will be provided with a marking schedule which you should check against your marked work.


In order to maintain satisfactory progress in ENGR 121, plan to spend about eleven hours a week during lecture times. One breakdown of this would be four hours in lectures, two hours in labs, one hour in a tutorial, two hours writing reports and assignments, and two hours reading and reviewing notes and tuts.

Teaching Plan

Communication of Additional Information

The course homepages on the web are the primary source of additional information. There will be links to these from Nuku and from ECS and SMS course list web pages. Lectures will be recorded to video, available from the next day through Nuku.

Offering CRN: 26052

Points: 15
Prerequisites: 16 Achievement Standard credits NCEA Level 3 in Mathematics) or (12 Achievement Standard credits NCEA Level 3 Mathematics excluding the statistics standards 91580, 91581, 91582, 91583, 91584) or MATH 132
Restrictions: Any pair (MATH 141/QUAN 111, MATH 151/161/177)
Duration: 27 February 2023 - 25 June 2023
Starts: Trimester 1
Campus: Kelburn