MASC 0010 Penn State University Engineering Mathematics Questions 7 questions on even-odd functions, Fourier series, fourier transform, z-transform and par

MASC 0010 Penn State University Engineering Mathematics Questions 7 questions on even-odd functions, Fourier series, fourier transform, z-transform and partial differential equation 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: ______________
= ______
= ( )
1) Classify the following function as even, odd or neither functions by showing the suitable
calculations:
a. 1 ( ) = ( cos(3 ))
(5 marks)
b. 2 ( ) = ( −1 + 3) sin ( )
(5 marks)
c. 3 ( ) =
( cos( +9))
sin( )+xM
d. 4 ( ) = ((3 − 1) −4 )
(5 marks)
(5 marks)
2) Find the in the Fourier series expansion of the function ( ) = 2 + 7 sin( ) defined
over the interval (− , ).
(20 marks)
( −1)
3) Show that ( ) = ( −2)( − )2 while solving the following difference equation by using Ztransform, and deduce it for the particular value of M.
+2 − 2 +1 + 2 = 2 , 0 = 0, 1 =
MEC_AMO_TEM_034_01
(15 marks)
Page 2 of 8
Engineering Mathematics 2(MASC 0010.1) – Spring – 20 – CW2 (Assignment) – All – QP
3 2 −
4) Find the inverse Z- transform of ( ) = ( −1)( −2 ).
(15 marks)
0
5) Show that the Fourier transform of function ( ) = {1
0