TEE 202/05 Engineering Mathematics II
Tutor-marked Assignment 2 (TMA 2 – 25%)

Evidence of plagiarism or collusion will be taken seriously and the University regulations will be applied fully. You are advised to be familiar with the University’s definitions of plagiarism and collusion.
Instructions:
This is an individual assignment. No duplication of work will be tolerated. Any plagiarism or collusion may result in disciplinary action, in addition to ZERO mark being awarded to all involved.
You must submit your TMA 2 online to the OAS system and it is your responsibility to submit your TMA correctly and timely. OAS system doesn’t allow re-submission of assignment so make sure you upload the correct file to OAS.
The total marks for TMA 2 is 100 and contributes 25% towards the total grade.
TMA 2 covers the topics in Unit 1, 2, 3 and 4.
TMA 2 has to be done individually.
Your assignment must be word processed (single spacing) and clearly laid out. You need to download and install the MathType equation editor uploaded in LMS into your computer, and use it to type your equations.
Since this is a mathematics assignment, all calculation steps must be clearly shown or full marks will not be awarded.
All files or documents submitted must be labelled with your WOU ID and your name.
Students are highly encouraged to passage their TMAs to the Turnitin system before submission, to encourage honest academic writing and it is not mandatory except for Project courses.
Question 1 (25 Marks)
Find the relative maximum and relative minimum points of the function, f(x,y)=x^2-y^3-12x+12y-13
[8 Marks]
Evaluate the Laplace transform of the following functions:
f(t)=sin?5t+e^2t
[5 Marks]
f(t)=t^2+cos?3t
[5 Marks]
Let f(t)=8t^5-5t^2+5t+1. Find L[(d^2 f)/(dt^2 )]
[7 Marks]
Question 2 (25 Marks)
Express (7s-6)/(s^2-s-6) in partial fraction form and then Find the inverse Laplace transform of (7s-6)/(s^2-s-6) using the partial fraction obtained.
[8 Marks]
Find the inverse Laplace transforms of (2s^2+5)/(s^2+3s+2)
[8 Marks]
Solve y^'' (t)+y(t)=cos??2t,? y(0)=0,y^' (0)=1 by using Laplace transform method.
[9 Marks]
Question 3 (25 Marks)
Find the z-transform of the following sequences:
{9k+7}_(k=0)^8
[5 Marks]
{5^k+k}_(k=0)^8
[5 Marks]
Find the inverse z-transform of the following:
Z^(-1) (2z/(z-2)^2 )
[5 Marks]
Z^(-1) (9z(z+3^2))/?(z-3^2)?^3
[5 Marks]
Z^(-1) (z(z+1^7))/?(z-1^5)?^3
[5 Marks]
Question 4 (25 Marks)
Find the Fourier Transform for the following function:
f(t)=f(x)={ ¦(10, t?0@0 , elsewhere)¦
[4 Marks]
Find the inverse Fourier transform of the following:
71/?
[5 Marks]
e^(-5j?)/((?^2+16))
[5 Marks]
1/(v? v2p (3+j?))
[5 Marks]
Find out whether the following functions are odd, even or neither:
sin?t+cos?t
[3 Marks]
x^4+x^6
[3 Marks]
END OF TMA 2