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Assignment Task :

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.

 

PART I:

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 , e.g., CBD ) with side lengths ofabc , ,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
a = 533,
b = 983,
c = 783,
d = 383 units
respectively).

Student City

 

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

City

 

PART II:

Airport

 

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 = 150 2 units .

ss1

 

Now, estimate the volume of the underground train tunnel by using Trapezoidal and Simpson’s 1/3rd rule. Comment on your finding

 

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  • Uploaded By : Grace
  • Posted on : July 06th, 2019

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