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MATH2167ProjectSem12021-2_-2119336200.pdf

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Written by: Dr. Silvana Delosevic Checked By: Mr. Selva Venkatesan

RMIT Classification: Trusted

Future Technologies, College of VE

Associate Degree in Engineering Technology (AD026)

Mathematics 1

MATH2167

Project

Sem 1 2021

1. The Project:

The project is an individual based task which requires students to apply principles of numerical

integration, Trapezoidal and Simpson’s 1/3 rd

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 25% to the total marks in this course.

3. Due date and instructions:

The project is to be completed and submitted through Canvas by Sunday 2 nd

May 2021, 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. Ensure that you address each criterion in your written responses.

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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 need to design land of your choice, named

Student Land. Then you need to find the area and volume by using Trapezoidal rule and or Simpson’s

1/3rd rule as indicated below.

Source: https://www.vecteezy.com/vector-art/146285-free-singapore-map-with-famous-landmark-vector

Figure 1: Land of your choice

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1. To sketch the design of the project, first draw a quadrilateral (base of your Student Land) as

shown in Fig. 2, 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 = 650 units + last 3 digits of your student number

b = 500 units + last 3 digits of your student number

c = 350 units + last 2 digits of your student number

d = 400 units + last 2 digits of your student number

(e.g. if your student number is 3054282 then a = 932, b = 782, c = 432, d = 482 units

respectively).

Figure 2.

1. Estimate the area of the base of the Student Land (quadrilateral), you sketched in (1), by using Trapezoidal rule and Simpson’s 1/3rd rule with any number of strips (at least 10 strips)

of your choice.

2. Now join the two end points of sides a, and c of the quadrilateral you sketched in part (1), by irregular curves (an example is shown in Fig 3.) to create the land of your choice named

Student Land.

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Figure 3.

Now estimate these two areas (areas you sketched outside the two sides a and c of the

quadrilateral) by using Trapezoidal rule with 11 strips (if addition of your student number is

an odd number) or by using Simpson’s 1/3rd rule with 12 strips (if addition of your student

number is an even number). Hence estimate the total area of the land and conclude your

findings.

Please note: Include drawing of Student Land (quadrilateral + extensions) and separate

drawing of quadrilateral (base of the Student Land) and drawing of each irregular shape area

(extensions). Subintervals and endpoints need to be clearly labeled on each drawing and

table with 𝑥 and 𝑦 has to be included.

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PART II: Trapezoidal Rule and Simpson’s 1/3rd Rule in finding

approximate volume

For transportation purposes undersea tunnel needs to be constructed to provide fast link

between the Student Land and X-Land, see Figure 4.

Figure 4.

A tunnel of length (𝑏 + 2000)𝑢𝑛𝑖𝑡 (similar to the Fig 5.) will be constructed to join the Student Land with X-Land. The thirteen cross sectional areas at regular intervals are: S0 = 220, S1 = 250, S2 = 280, S3 = 300, S4 = 330, S5 = 365, S6 = 395, S7 = 415, S8 = 435, S9 = 455, S10 = 475, S11 =

490, S12 = 530 2

units .

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Figure 5.

Now estimate the volume of undersea tunnel by using Trapezoidal and Simpson’s 1/3rd rule.

Comment on your findings.

Figure 5: Underwater tunnel across the Bosporus connecting Asian and European side of Istanbul

Source: https://www.dailysabah.com/business/2014/04/14/underwater-digging-begins-for-2nd-bosporus-tunnel

Note: The figures are just shown as examples without considering the scales. You need to scale

properly for all your graphs/sketches.

https://www.dailysabah.com/business/2014/04/14/underwater-digging-begins-for-2nd-bosporus-tunnel