SOLUTION: MASC 0010 Penn State University Engineering Mathematics Questions

Engineering Mathematics 2(MASC 0010.1) – Spring – 20 – CW2 (Assignment) – All – QP
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IN SEMESTER INDIVIDUAL ASSIGNMENT
Module Code: MASC 0010.1
Module Name: Engineering Mathematics 2
Level: 2
Max. Marks: 100
Instructions to Student

Answer all questions.

Scientific calculators are permitted to use.

Use the suitable formulas as required.

Deadline of submission: 09/07/2020 23:59

The marks received on the assignment will be scaled down to the actual weightage
of the assignment which is 50 marks

Formative feedback on the complete assignment draft will be provided if the draft is
submitted at least 10 days before the final submission date.

Feedback after final evaluation will be provided by 23/07/2020
Module Learning Outcomes
The following LOs are achieved by the student by completing the assignment successfully
1.
2.
3.
Use transforms methods to solve the difference equations.
Construct Fourier series expansions for input and steady-state output signals in both
trigonometric and complex exponential forms.
Forming and solving partial differential equations
Assignment Objective
The aim of this assignment to test the understanding of the students on various integral transform
operators. This also include testing their knowledge on the procedure and accuracy on the topics of
Fourier analysis. The computational ability of the students in forming and solving a partial differential
equation will also be tested.
MEC_AMO_TEM_034_01
Page 1 of 8
Engineering Mathematics 2(MASC 0010.1) – Spring – 20 – CW2 (Assignment) – All – QP
Assignment Tasks
Write your MEC student ID: ______________
𝑴 = ______ 𝒍𝒂𝒔𝒕 𝒅𝒊𝒈𝒊𝒕 𝒐𝒇 𝒚𝒐𝒖𝒓 𝑴𝑬𝑪 𝑰𝑫
𝑴 = 𝒔𝒆𝒄𝒐𝒏𝒅 𝒍𝒂𝒔𝒕 𝒅𝒊𝒈𝒊𝒕 𝒐𝒇 𝒚𝒐𝒖𝒓 𝑴𝑬𝑪 𝑰𝑫 (𝒊𝒇 𝒆𝒏𝒅𝒊𝒏𝒈 𝒘𝒊𝒕𝒉 𝟎)
1) Classify the following function as even, odd or neither functions by showing the suitable
calculations:
a. 𝑓1 (𝑥) = (𝑥 𝑀 cos(3𝑥))
(5 marks)
b. 𝑓2 (𝑥) = (𝑥 𝑀−1 + 3) sin𝑀 (𝑀𝑥)
(5 marks)
c. 𝑓3 (𝑥) =
(𝑒 𝑀𝑥 cos(𝑀𝑥+9))
sin(𝑀𝑥)+xM
d. 𝑓4 (𝑥) = ((3𝑥 − 1)𝑀−4 )
(5 marks)
(5 marks)
2) Find the 𝑎𝑛 in the Fourier series expansion of the function 𝑓(𝑥) = 𝑀𝑥 2 + 7 sin(𝑀𝑥) defined
over the interval (−𝜋, 𝜋).
(20 marks)
𝑀𝑧(𝑧−1)
3) Show that 𝐹(𝑧) = (𝑧−2)(𝑧−𝑀)2 while solving the following difference equation by using Ztransform, and deduce it for the particular value of M.
𝑦𝑘+2 − 2𝑀𝑦𝑘+1 + 𝑀2 𝑦𝑘 = 𝑀 2𝑘 , 𝑦0 = 0, 𝑦1 = 𝑀
MEC_AMO_TEM_034_01
(15 marks)
Page 2 of 8
Engineering Mathematics 2(MASC 0010.1) – Spring – 20 – CW2 (Assignment) – All – QP
3𝑧 2 −𝑀𝑧
4) Find the inverse Z- transform of 𝐹(𝑧) = (𝑧−1)(𝑧−2𝑀).
(15 marks)
0
5) Show that the Fourier transform of function 𝑓(𝑡) = {1
0
𝑡
Outstanding
Reflection and critical
analysis.
Highly competent analytical
skills and reflective practice,
demonstrating
personal
learning and growth, insight
into required professional
values and principles and
professional development
planning.
Knowledge and
Understanding/
Application of Theory
Extensive knowledge and
depth of understanding of
principles and concepts and
/or outstanding application
of theory in practice.
Evidence of Reading
Referencing and
Bibliography
Presentation, Grammar and
Spelling
Evidence of reading an
extensive range of
educational
literature/research and
where applicable workplace
strategies, policies and
procedures.
Accurate referencing and
bibliography correctly using
appropriate referencing
style
Excellent presentation,
logically structured, using
correct grammar and
spelling, excellent crossreferencing and links to
supporting evidence
Strong analytical skills and
reflective practice used,
demonstrating
personal
learning and growth, insight
into required professional
values,
principles
and
competencies
and
professional development
planning.
Excellent knowledge and
understanding of principles
and concepts and /or
excellent knowledge and
understanding
of
the
application of theory in
practice
Evidence of reading a wide
range
of
educational
literature/research
and
where applicable, workplace
strategies, policies and
procedures.
Appropriate referencing and
bibliography correctly using
appropriate
referencing
style
Good
presentation,
competently
structured,
using correct grammar and
spelling, clear and easy to
use links to supporting
evidence
Good knowledge or key
principles and concepts
and/or good knowledge of
the application of theory in
practice
Evidence of reading a good
range
of
educational
literature/research
and
where applicable workplace
strategies, policies and
procedures.
Generally well referenced
with correct use of the
appropriate
referencing
style
Very Good Quality
Good use of analytical skills
and
reflective
practice
demonstrating
personal
learning and growth, insight
into required professional
values,
principles
and
competencies
and
professional development
planning.
Reasonable presentation,
completely
structured,
acceptable grammar and
spelling, acceptable links to
supporting evidence
Acceptable knowledge of
key principles and concepts
and/or knowledge of the
application of theory in
practice
Evidence of reading an
appropriate
range of
educational
literature/research
and
where applicable, relevant
workplace policies and
procedures
Adequate
referencing.
Generally accurate use of
appropriate
referencing
style
Good (Acceptable)
Acceptable use of analytical
skills and reflective practice
demonstrating
personal
learning and growth, insight
into required professional
values,
principles
and
competencies
and
professional development
planning.
Adequate presentation and
structure,
acceptable
grammar and spelling,
adequate links to supporting
evidence
Adequate knowledge of key
principles and concepts
and/or satisfactory evidence
of the application of theory
in practice.
Evidence of minimal reading
of
educational
literature/research
and
where applicable relevant
workplace policies and
procedures
Adequate
referencing.
Appropriate
referencing
style used but may contain
some inaccuracies.
Weak
presentation
,
satisfactory
structure,
grammar and spelling, links
to supporting evidence
Adequate/ Satisfactory
Adequate use of analytical
skills and reflective practice
demonstrating
personal
learning and growth, insight
into required professional
values,
principles
and
competencies
and
professional development
planning.
Little use of analytical skills
and
reflective
practice
demonstrating
personal
learning and growth, insight
into required competencies
and/or
professional
development
planning.
Professional values and
principles not reflected in
the submission.
Little evidence of knowledge
of key principles or concepts
and/or little evidence of the
application of theory in
practice
Little or no evidence of
reading outside of the
course textbook and/or
reference to relevant work
place policies and
procedures
Little or no referencing,
incorrect style, or very
inaccurate use of
appropriate referencing
style
Poor presentation, grammar
and spelling, links to
supporting evidence
Excellent
Weak /Poor
(all learning outcomes not
adequately met)
and/or
Insufficient/no
use
of
analytical
skills
and
reflective
practice
demonstrating
personal
learning and growth, insight
into required competencies
and
professional
development planning
MEC_AMO_TEM_034_01
and/or
and/or
No evidence of knowledge
of key principles or concepts
and/or no evidence of
application of theory in
practice
No evidence of reading
outside of the course
textbook and/or reference
to relevant workplace
policies and procedures
and/or
Unacceptable presentation,
grammar and spelling,
structure is very poor, links
to supporting evidence
Page 8 of 8

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