Written by: Dr. Silvana Delosevic
Checked By: Mr. Selva Venkatesan
College of Science, Engineering and Health
School of Vocational Engineering, Health and Sciences
Associate Degree in Engineering Technology (AD026)
Mathematics 1
MATH2167
Project
Sem 1 2020
1. The Project:
The project is an individual based task which requires students to apply principles of numerical
integration, Trapezoidal and Simpson’s 1/3rd rule, to real life situations. You are required to analyse
the problems and provide detailed solutions explaining your interpretation and reasoning clearly,
taking care that your answers and explanations are original, appropriately referenced and all
working is shown clearly. Include graphs, tables and sketches wherever relevant to illustrate your
explanations.
2. Assessment:
The project contributes 20% to the total marks in this course.
3. Due date and instructions:
The project is to be completed and submitted through Canvas by Sunday 3rd of May 2020, 23:59.
The report should include a cover page with your full name, student number, group name, course
name, assessment title, and submission date. Solution to each problem should include an
introduction which outlines the problem in your own words, mathematical solution which should
be accompanied by a written explanation at each step, and a conclusion should explain your
findings in the context of the problem.
4. Assessment Criteria:
The project will be assessed according to the Performance descriptors and ratings rubric given
in the Assessment Section (Project) of the Canvas .
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All rights reserved. Apart from any use permitted under the Copyright Act 1968 no part may be reproduced, stored in a retrieval system
or transmitted by any means or process whatsoever without the prior written permission of the RMIT University.
PART I: Trapezoidal Rule and Simpson’s 1/3rd Rule in finding
approximate area
Trapezoidal rule and or Simpson’s 1/3rd rule are commonly used to find the approximate surface area
of the lands or some irregular surfaces. In this project you will need to design an urban city of your
choice named Student’s City.
Then you will need to find the area and volume by using Trapezoidal rule and or Simpson’s 1/3rd rule
as indicated below.
1. To sketch the design of the project first draw a quadrilateral (base of your city as shown in
Fig 1., e.g., CBD ) with side lengths of a b c , , and d units on a graph paper by hand, or
by using some appropriate graphing/drawing software, e.g., AutoCAD, GeoGebra,…,
where lengths of the sides are:
a = 450 units + last 2 digits of your student number
b = 700 units + last 3 digits of your student number
c = 500 units + last 3 digits of your student number
d = 300 units + last 2 digits of your student number
| (e.g. if your student number is 3654283 then respectively). |
= 533, = 983, = 783, = 383 units |
a b c d
Copyright © [2019] RMIT University
All rights reserved. Apart from any use permitted under the Copyright Act 1968 no part may be reproduced, stored in a retrieval system
or transmitted by any means or process whatsoever without the prior written permission of the RMIT University.
Figure 1.
1. Estimate the area of the base of the city (quadrilateral), you sketched in (1), by using
Trapezoidal rule and Simpson’s 1/3rd rule with any number of strips (at least 8) of your
choice. However, when using the Simpson’s rule, you need to take even number of strips.
2. Now extend the city by adding industry zone and airport by joining the two end points of
sides d and c of the quadrilateral you sketched in part (1), by irregular curves (an example is
shown in Fig 2. and Fig 3.) to create the city of your choice.
Figure 2.
Copyright © [2019] RMIT University
All rights reserved. Apart from any use permitted under the Copyright Act 1968 no part may be reproduced, stored in a retrieval system
or transmitted by any means or process whatsoever without the prior written permission of the RMIT University.
Figure 3.
Now estimate these two areas (areas you sketched outside the two sides d and c of the
quadrilateral) by using Trapezoidal rule with 9 strips (if the sum of the digits of your student
number is an odd number) or by using Simpson’s 1/3rd rule with 10 strips (if the sum of the
digits of your student number is an even number). Hence, estimate the total area of the land
and conclude your findings.
Please note: The drawings of the quadrilateral and the two irregular shapes should be shown
separately.
Copyright © [2019] RMIT University
All rights reserved. Apart from any use permitted under the Copyright Act 1968 no part may be reproduced, stored in a retrieval system
or transmitted by any means or process whatsoever without the prior written permission of the RMIT University.
PART II: Trapezoidal Rule and Simpson’s 1/3rd Rule in finding
approximate volume
For transportation purposes underground train tunnel needs to be constructed under the
quadrilateral, base of the city, i.e., CBD to provide fast link around the city, see Fig. 4 and 5.
Figure 4.
Figure 5.
Copyright © [2019] RMIT University
All rights reserved. Apart from any use permitted under the Copyright Act 1968 no part may be reproduced, stored in a retrieval system
or transmitted by any means or process whatsoever without the prior written permission of the RMIT University.
A tunnel of length ( 300) d + units (see Fig 6.) will be constructed under the base of the city
(quadrilateral), i.e., CBD. The nine cross sectional areas at regular intervals are: S0 = 100, S1 =
112, S2 = 113, S3 = 120, S4 = 125, S5 = 130, S6 = 140, S7 = 145, S8 = 150units 2 .
Figure 6.
Now, estimate the volume of the underground train tunnel by using Trapezoidal and Simpson’s 1/3rd
rule. Comment on your findings.
Note: The figures are just shown as examples without considering the scales. You need to scale
properly for all your graphs/sketches.
Reference list:
Images: https://www.vecteezy.com/vector-art
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