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

3Maldives Business School Cover PageASSESSMENT BRIEFBachelor’s Degree Year 1The student must fill the relevant parts of the following table.Student First Name Student Last Name Student ID Task No. Date...BBMM103 Management Principles: Case StudyPolaroid - Disruptive Innovation!*The following case study has been written drawing heavily on the information both from the Boston.com Staff website and the official...Task 2: Office quizJohn Canon, the branch manager, runs a monthly training session with the sales team. This month he has set a quiz to check the salespeople’s understanding of the Real Estate Agents Act...ASSESSMENT BRIEFSubject Code and Title PROJ6000 Principles of Project ManagementAssessment Assessment 3 – Visual Presentation: ProjectManagement Processes, Methodologies and Knowledge AreasIndividual/Group...Assessment 1 – ResearchInstructions:This is an individual and in-class assessment.You need to write answer for all the tasks successfully to get “Satisfactory” in this assessment. Trainer will provide...Summary:Write a summative paper on seminal theories of governance and stewardship that inform effective organizational leadership in non-profit or for profit organizations. Your assertions should be supported...r7 Assessment Task 3 Instructions VocationalTr.InIng InilltutoComplete the following activities: 1, Research technology and tools that managers can use lo manage their work priorities.You should research...**Show All Questions**