ENGEN102-22B (SEC)

Engineering Maths and Modelling 1B

15 Points

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Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics


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: maria.admiraal@waikato.ac.nz

Placement/WIL Coordinator(s)


Student Representative(s)

Lab Technician(s)


: cheryl.ward@waikato.ac.nz

You can contact staff by:

  • Calling +64 7 838 4466 select option 1, then enter the extension.
  • Extensions starting with 4, 5, 9 or 3 can also be direct dialled:
    • For extensions starting with 4: dial +64 7 838 extension.
    • For extensions starting with 5: dial +64 7 858 extension.
    • For extensions starting with 9: dial +64 7 837 extension.
    • For extensions starting with 3: dial +64 7 2620 + the last 3 digits of the extension e.g. 3123 = +64 7 262 0123.
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Paper Description

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The paper covers.

  • Functions and trigonometric equations
  • More calculus, particularly integration, with applications to engineering problems.
  • An introduction to statistics
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Paper Structure

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Each week students should

  • watch/attend all 3 lectures.
  • watch/attend the weekly workshop.
  • attend and actively participate in a one hour tutorial.
  • do (and submit) the weekly assignment and workshop assessment
  • put in at least 5 additional hours of study.
  • watch moodle for notices and supplementary material.

Lectures will be recorded and available on panopto. While SEC students are likely to be participating remotely (over the internet), students based in Hamilton or Tauranga are welcome to attend on-campus lectures, tutorials, and workshops, if they wish to do so and can fit it into their school timetable.

Note the actively participate. This is key for your success in this paper. Engineering maths is not a spectator sport---you learn by doing.

If covid alert levels change some of these activities may only be available online. Details will be provided as needed.

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Learning Outcomes

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Students who successfully complete the paper should be able to:

  • The learning outcomes for this paper are linked to Washington Accord graduate attributes WA1-WA11.

    Explanation of the graduate attributes can be found at: https://www.ieagreements.org/

    • Demonstrate understanding of mathematical ideas and notation in calculus and statistics:

      Understand foundational mathematical concepts, notation and ideas to a sufficient level to recognise, understand and work with these concepts as they arise in engineering texts, applications, and other engineering papers. (WA1, WA9, WA11)

    • Recognise the application of mathematics, especially calculus and statistics, to engineering applications:

      Appreciate how these ideas can be used as a tool in an engineering context and thus formulate an appropriate mathematical description of engineering problems. (WA2, WA4)

    • Use appropriate mathematical tools from calculus and statistics to solve problems:

      Recognise and use appropriate mathematical techniques to solve engineering problems formulated in mathematical terms (WA3, WA5)

    Linked to the following assessments:
    Assignments, including questions set from the textbook (1)
    Test 1: Please ensure you are available. (2)
    Test 2: Please ensure you are available. (3)
    Final test: in the 2-week exam period. D rule applies (4)
  • Some things you should _ALREADY_ be able to do
    • State the definition of the derivative and give physical/geometrical interpretations of it.
    • Know how to use basic rules of differentiation (eg, sum, product, quotient, chain) to differentiate functions.
    • Integrate elementary functions (polynomials, trig fns, exponential function)
    • Calculate basic statistics such as mean, median, standard deviation and quartiles
    Linked to the following assessments:
  • Some specific objectives for the paper are. Calculus/Algebra:
    • Setup and solve trigonometric equations.
    • Describe features of waves and oscillations (amplitude, period, wavelength, phase, phase difference, ...)
    • Describe what a function is/does. Be able to draw its graph. Decompose a function into even and odd parts.
    • Apply differentiation to determine the maximum and minimum of functions, solve "related rates" problems, including in engineering applications, and produce accurate sketches of functions.
    • Be able to calculate Taylor series for simple functions.
    • Calculate indefinite and definite integrals of simple functions. Interpret integrals.
    • Be able to integrate using the methods of substitution, integration by parts, and partial fractions. Be able to recognize which technique to use.
    • Use integration to help setup and solve engineering applications and problems.
    • Know and use properties of the logarithm and exponential functions, particularly in solving engineering-based problems.
    • Solve problems involving first-order separable differential equations.
    • Know basic properties of the conic sections (circle, ellipse, hyperbola, parabola)
    • Understand and use the integral definition of the average of a function.
    Linked to the following assessments:
  • Statistics
    • Calculate measures of location and spread
    • Calculate probabilities using the normal distribution
    • Understand key statistical theories - the strong law of large numbers and the central limit theorem
    • Perform statistical inference procedures for means - hypothesis tests and confidence intervals
    Linked to the following assessments:
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NOTE: If covid-related restrictions (eg lockdowns) mean that in-person assessment is no longer possible we may move everything online. Should this happen we reserve the right to (i) adjust the weightings of each assessment item in whatever fashion seems appropriate, and (ii) change the due dates for any assessment items. How the weights change will depend on what changes we are forced to make and when during the trimester this happens.

Your final grade is determined from your performance in TWO in-trimester Tests, a FINAL TEST, and a total tutorial component (including weekly assignments).
All three tests must be supervised by a teacher (or taken at the Hamilton campus at the same time as the MATHS101(HAM) class take the test). During these tests, students shall not use or have access to the internet, phones, laptops, smart watches, etc.
The FINAL TEST, held in the B trimester exam period, is a compulsory item of assessment.

Assignment sheets will be available each week, via moodle.

See the table below for Test dates and assessment weightings.

For identification purposes you must take your student ID Card to each test and show it to the test supervisor. If you do not, your test mark will not be counted until we cannot verify that it was you who sat the test.

The D rule: An UNRESTRICTED pass (i.e. C- or better) will only be awarded to students who achieve both a final overall mark of at least 50% and a Final Test mark of at least 40%. There will be no test resits.

The tutorial/assignment component.

  • There will be 11 assignments and the best 9 marks will be counted. Assignments should be your own work and copying may lead to a referral to the university disciplinary committee. Essentially, there is an assignment to hand in every week.
  • Each weekly assignment sheet will also include tutorial problems. There is no need to hand these in, although you are encouraged to do all of these. Practicing problem solving will improve your chances of doing well in this paper.
  • The best n-2 out of n policy is intended to allow students to miss one or two assignments due to illness or other good reason without requiring us to process medical certificates. Where serious illness may cause a more prolonged absence, please consult the lecturer.
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Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 100:0. There is no final exam. The final exam makes up 0% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 100:0 or 0:0, whichever is more favourable for the student. The final exam makes up either 0% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. Assignments, including questions set from the textbook
  • Online: Submit through Moodle
2. Test 1: Please ensure you are available.
22 Aug 2022
No set time
3. Test 2: Please ensure you are available.
10 Oct 2022
No set time
4. Final test: in the 2-week exam period. D rule applies
Assessment Total:     100    
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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Required and Recommended Readings

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Required Readings

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HIgher Engineering Mathematics (9th edition). John Bird. Routledge 2021.

Assignment problems will be set from this text so you will need access to a copy.
The university library has online versions of this edition. In other editions, the explanations/text will be fine to use, but don't assume the problem numbers will match.

NOTE: Using/buying second-hand copies of text books is a fine idea.

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Recommended Readings

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You may like to look at alternative presentations of the same material.

  • Schaum’s Outlines ‘Calculus’, Ayres & Mendelson, McGraw-Hill. This is the MATHS101 textbook and has many worked examples.
  • Engineering Mathematics, K. A. Stroud (with Dexter J. Booth), 7th Edition, Industrial Press, Inc. This was used in previous year. It is a good book for working through, but more difficult to dip into.
  • Engineering Mathematics, Kreyszig, etc
  • Modern Engineering Mathematics, Glyn James, Pearson (2015 version available as an e-book via the library).
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Other Resources

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The only type of calculator you may use in the tests or the exam is a CASIO 82 variant (as used in ENGEN101). The CASIO 82 Au Plus II is a recent member in this series of calculators. If you bring a graphing or CAS calculator to a test or the exam you will not be permitted to use it.

Microsoft Excel may be used to perform tasks in the statistics part of the course. Microsoft Office 365 is available and free to all enrolled University of Waikato students. Instructions to download can be found through the following link:


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Online Support

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The Moodle page for this paper is the main forum for notices and information about the course. Assignments are posted on Moodle. The gradebook for this paper can also be accessed through Moodle. It is your responsibility to check your marks are correctly entered.

Lectures will be available online (panopto recordings). These can be accessed via the Moodle page.

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There are 5 'contact' hours each week consisting of 3 lectures, 1 workshop and 1 tutorial. Students should attend these AND spend an additional 5 hours per week in study, including doing the assignments and reading the textbook.
Additional time should be spent in preparation during study week and for tests. Altogether students should expect to commit 150 hours across the trimester for this paper. Students who are not well prepared may need more time.

Doing all the assignments questions AND all the tutorial questions is strongly recommended. Doing this is likely to substantially improve your understanding (and grade).

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Linkages to Other Papers

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Prerequisite papers: ENGEN101




Restricted papers: MATHS101, MATHS102, ENGEN183, ENGEN184

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