EE212 Old Exams2

8/3/2019 EE212 Old Exams2

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EE 212/01 Examination No. 2 Spring 2009/10

Kuwait University

Electrical Engineering Department

Name in Arabic :

Student I. D. : .

Signature : .

Problem No. Grade

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Problem 1:

a) (20 points): Use () () to find the Fourier transform of() { ?

b) (2.5 points): Sketch the amplitude spectrum?c) (2.5 points): Sketch the phase spectrum?

Problem 2 (25 points): Find the temperature () in a laterally insulated bar of thermal diffusivity and length . The bar has initial temperature() and is kept at at the ends

Problem 3a) (10 points): Use the Cauchy-Riemann equations to tell if() ( ) is analytic or

not?

b) (15 points): Find all solutions z of ?

Problem 4 (25 points): Integrate counterclockwise around the triangle with vertices z= 0, 2,2+2i ? ( is the complex conjugate of z)


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EE 212/01A Examination No. 2 Summer 2011

Kuwait University


Name :

Student I. D. : .

Signature : .

Problem No. Grade

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Problem 1: Use the properties of the Fourier transform to find the Fourier transform of() ()?

Problem 2: Convert the ordinary differential equation ( ) to the Legendreequation by using

then find the solution

()

Problem 3

c) (10 points): Use the Cauchy-Riemann equations to show that() is analytic for all ?d) (15 points): Find all solutions z of

?

Problem 4: Use the Residue theorem to evaluate () counterclockwise around theclosed path C: circle of radius 2 with center at origin?


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EE 212/51 Examination No. 2 Fall 2010/11

Kuwait University


Name :

Student I. D. : .

Signature : .

Problem No. Grade

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Problem 1: Find the exponential Fourier series of the following function (simplify your final answer as

much as possible) and sketch its exponential spectra for ?Hint for

Problem 2: The steady state temperatures in the rectangle plate ( ) can bedescribed by the Laplace equation ( ) () () . Let thetemperature ( ) on the upper side and ( ) on the other three sides of the rectangleplate. Find the steady state temperature at ?Problem 3: Reduce the differential equation () () ( ) toBessels equation by using

then find the solution

()with a free parameter

?

Problem 4 Use the Cauchy-Riemann equations toshow that the complex function() () is analytic then find all solutions of() ?

()

EE212 Old Exams2

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