ENGEN102-21B (TGA)

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

Staff

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Convenor(s)

Ajit Pal Singh

Ajit Pal Singh
3533
TCBD.4.02
See Moodle
ajitpal.singh@waikato.ac.nz

Lecturer(s)

Chanelle Gavin

Chanelle Gavin
3532
TCBD.4.02
See Moodle
chanelle.gavin@waikato.ac.nz

Administrator(s)

Placement/WIL Coordinator(s)

Tutor(s)

Student Representative(s)

Lab Technician(s)

Librarian(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

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

Lectures will be recorded and available on panopto. Our recommendation is to use the recordings in addition to attending the lectures in person.

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:

  • 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:
  • Setup and solve trigonometric equations
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 1 (3)
    • Exam (5)
  • Describe features of waves and oscillations (amplitude, period, wavelength, phase, phase difference, ...)
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 1 (3)
  • Describe what a function is/does. Be able to draw its graph. Decompose a function into even and odd parts.
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 1 (3)
  • Apply differentiation to determine the maximum and minimum of functions, solve "related rates" problems, including in engineering applications, and produce accurate sketches of functions.
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 2 (4)
    • Exam (5)
  • Be able to calculate Taylor series for simple functions
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 2 (4)
    • Exam (5)
  • Calculate indefinite and definite integrals of simple functions. Interpret integrals
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 1 (3)
    • Exam (5)
  • Be able to integrate using the methods of substitution, integration by parts, and partial fractions. Be able to recognize which technique to use
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 1 (3)
    • Exam (5)
  • Use integration to help setup and solve engineering applications and problems
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 1 (3)
    • Exam (5)
  • Know and use properties of the logarithm and exponential functions, particularly in solving engineering-based problems
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 1 (3)
  • Solve problems involving first-order separable differential equations
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 2 (4)
    • Exam (5)
  • Know basic properties of the conic sections (circle, ellipse, hyperbola, parabola)
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Exam (5)
  • Understand and use the integral definition of the average of a function
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Exam (5)
  • Statistics

    Linked to the following assessments:
  • Calculate measures of location and spread
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Test 2 (4)
    • Exam (5)
  • Calculate probabilities using the normal distribution
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Exam (5)
  • Understand key statistical theories - strong law of large numbers and the central limit theorem
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Exam (5)
  • Perform statistical inference procedures for means and proportions - hypothesis tests, confidence and prediction intervals
    Linked to the following assessments:
    • Workshops (1)
    • Assignments (2)
    • Exam (5)
  • 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:
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Assessment

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The assessment items are listed here. For the percentage contributions of these to the final mark, see the table a little further down.

TWO Tests.
See table below for dates. Please ensure you are available for these dates and times. Alternative dates/times will not be available. Tests will be held on-campus (unless covid alert levels do not allow this).

If Covid alert levels change, a test may be given online and the test dates may be changed from those listed in the table below.

There will be NO test resits.

A workshop grade.

  • There will be 12 workshops with quizzes to be completed at each. The best 10 will be counted. This is an in-class assessment in which working in pairs is encouraged.

A 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.

A FINAL EXAM, held in the B trimester exam period. This is a compulsory item of assessment.

In order to pass this paper with an unrestricted grade (Grade C- or better) you must get an overall total of 50% or greater, and ALSO at least 40% in the final exam (the D rule).

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Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 50:50. There is no final exam. The final exam makes up 50% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 50:50 or 0:0, whichever is more favourable for the student. The final exam makes up either 50% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. Workshops
5
  • In Class: In Workshop
2. Assignments
15
  • Hand-in: In Tutorial
3. Test 1
16 Aug 2021
6:00 PM
15
4. Test 2
6 Oct 2021
6:00 PM
15
5. Exam
50
✔
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 (8th edition). John Bird. Routledge 2017.

Assignment problems will be set from this text so you will need access to a copy.
The university library has online versions of other editions. The explanations in these 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.

  • 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.
  • Schaum’s Outlines ‘Calculus’, Ayres & Mendelson, McGraw-Hill. This is the MATHS101 textbook and has many worked examples
  • 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:

https://www.waikato.ac.nz/ict-self-help/guides/free-microsoft-office-suite-download

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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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Workload

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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(s)

Prerequisite papers: ENGEN101

Corequisite(s)

Equivalent(s)

Restriction(s)

Restricted papers: MATHS101, MATHS102, ENGEN183, ENGEN184

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