Technology Mathematics & Computing

This assignment designed to assess your ability to formulate simple mathematical problems in engineering and to use the computer

algebra package Maple and Excel for solving them (it is worth 15% of the module mark).

You must use Maple for Tasks 1 and 2 and Excel for Task 3. Marks will belost if you carry out calculations on paper or with a

calculator and type in the results.Please make sure your answer to each question is very clear to the marker and use comments as

necessary to describe important intermediate steps in the solutions. Marks will be given for the worksheets functioning correctly and

will also be awarded for clarity of the work. Pleasedon’t share files, or email worksheets to each-other. Any attempt to do so will be

treated as academic misconduct. Be aware of the University rules on plagiarism:

https://mykingston.kingston.ac.uk/myuni/academicregulations/Pages/plagiarism.aspx

Submission Details
The deadline for this assignment is 10 AM on 28thJanuary 2016. Late submissions within 1 week will be capped at 40%.
Please use a new file for each question, so three files should be submitted. Start each by entering your name and ID number then save

your files (worksheets) in your normal directory.

Name your files as follows:
Maple file – as your ‘kunumberTask1.mw’ file and ‘kunumberTask2.mw’, submitted via the Study-Space drop box before the

deadline.
Excel file – as your ‘kunumberTask3.xlsx’ file, submitted via Study-Space drop box before the deadline.
You must also submit a printed copy of all files (including a signed submission sheet) in the box outside the Student Office

(SB34) by this same deadline.

Important- once you have submitted your file to Study-Space, do NOT open that file again until you have been given your mark for the

coursework. This is a safeguard against the event that the files are not readable by the marker.
Task 1 – Maple Task
The construction roads and railways must take into account the ‘sharpness’ of the bends in relation to the speed of the vehicles which

will be using them. For these constructions, considerations of comfort and safety will be paramount (although discomfort and perceived

lack of safety might be the designers’ wish for curves on a big adventure park ride). This task introduces you to a way of quantifying

the ‘sharpness’ of curves in a function f(x) by what is defined as the signed curvature κ of the function, given by
κ=f^”/(1+〖〖(f〗^’)〗^2 )^(3/2)
Use Maple to create the first and second derivatives of f(x)=x^2 (note that the result produced by differentiation is an

expression so you may find it helpful to use the unapply command from Worksheet 1 to create functions for these derivatives).

(10 marks)
Find the curvature of the function at x=0and x=1 then plot the function f(x)=x^2. Comment briefly in your file what you can say

about the comparative sharpness of the curve at these two points. (15 marks)
Plot the curvature of the function for all values of x from -2 to 2. Add another comment to your file describing what you

observe about the curvature over this range (perhaps think what curvature a straight line would have).
(15 marks)
Task 2 – Maple Task
A circular plot of land of radius ris available for the construction of a building with a rectangular floor plan. The rectangular

footprint of the building must meet the circular plot perimeter at its 4 corners. Use Maple to find the values of x and y (in terms of

r) which will give a maximum area for the building floor plan. Confirm using calculus that this optimal solution found is indeed a

maximum.
(25 marks)
Task 3 – Excel Task
Trigonometric functions are important in engineering as these describe oscillating behaviour so their correct calculation is of great

importance. There are built-in functions in Excel for this, but here you are asked to calculate them in terms of the following series

representations.

Note that to help you the general form of each term (the ones involving n) is given and that the first term of the series in each case

is given by n=0, the second by n=1 etc.

What you are to investigate here is how many terms of the series are needed to give a good approximation to the true values of the two

functions when measured against Excel’s built-in sine and cosine functions.

The layout you are to use In Excel is as follows:

You are to produce an Excel file with the same headings as above. The sine and cosine series columns are to contain the running totals

of the values resulting from the two formulae given above, whilst the Tan(x) series must be created from these sine and cosine results.

There is also a column of relative errorsin the tangent series which must be calculated by comparison with the built-in Tan(x) function

value at the top of the table. In addition:
Use Excel’s Data Validation to keep the angle x input between values where tan(x) remains finite (the box showing in the above

screenshot is the error message that you must define and which will display when the input cell for x is active)
Format all the cells in the table to write to 10 decimal places (you may need to widen some columns if they display a row of

hashes #####)
You must use absolute referencing (using the $ symbol) wherever appropriate so that in your completed spreadsheet everything

updates if you just want to change the x value.
(35 marks)

TAKE ADVANTAGE OF OUR PROMOTIONAL DISCOUNT DISPLAYED ON THE WEBSITE AND GET A DISCOUNT FOR YOUR PAPER NOW!