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

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

BLAW EssayPart A (1000 words)Question 1 Analyse the law(Suggested cases)Ermogenous v Greek Orthodox Church of SA:*Jones V Padavattan,* Todd V Nicol*Rose & Frank V Crampton case ….---What is the legal...referencing: Havard styleYour Task• You are required to prepare a business letter to answer all of the following questions.• You are also required to prepare a short video presentation (3 to 5 mins) summarising...HPS307 AT2 Personality Profile ReportName:1) Interpret/describe your personality profile using all of the IPIP and HEXACO factors, and the HEXACO facets that are of interest to you. Consider how well the...Individual Reflective Journal SpecificationsWord limit: 1000Purpose:The Individual Reflective Journal is to ensure each student is able to provide a critical reflection oftheir personal learning process,...Individual Assignment SpecificationsPurpose:This assignment aims at developing your understanding of the purpose and use of Management Accounting Systems (MAS) and its usefulness in aiding managers make...Attached if the information on the Literature Review I need done please. 2000 words Not Including the referencing. There are 3 topics to choose from and a template to write in please read all information...Attatched if the information on the Literature Review I need done please. 2000 words Not Including the referencing. There are 3 topics to choose from and a template to write in please read all information...**Show All Questions**