Download JNTUA B.Tech 1-2 R15 2019 June 15A54201 Mathematics ? II Question Paper

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MATHEMATICS ? II
(Common to all)

Time: 3 hours Max. Marks: 70

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PART ? A
(Compulsory Question)

*****
1 Answer the following: (10 X 02 = 20 Marks)

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(a) State sufficient conditions for the existence of Laplace transform.

(b) Find ? ? 1
?cot
? 1

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?
? 2
? ?.
(c) Find the half range sine series for ? ( ? ) = 1 ? (0, ? ).
(d) Define complex form of Fourier series.

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(e) Find the Fourier cosine transform of the function ? ( ? ) = ?
? ? ? , 0 < ? < ? 0, ? > ? .
(f) State Fourier integral theorem.
(g) A rod 30 cms long has its ends A and B kept at 20

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o
C and 80
o
C respectively until steady state is
prevailed. Determine the steady state temperature of the rod.

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(h) Form the PDE by eliminating the arbitrary constant from ? = ( ? 2
+ ? 2
)( ? 2
+ ? 2
).

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(i) State initial value theorem on z-transform.

(j) Find ? ?
1
? + 1

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?.

PART ? B
(Answer all five units, 5 X 10 = 50 Marks)

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UNIT ? I

2 (a) Use convolution theorem to find ? ? 1
?
? 2

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( ? 2
+ ? 2
)( ? 2
+ ? 2
)

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?.
(b) Find the Laplace transform of the triangular wave of period 2a given by:
? ( ? ) = ?
? , 0 < ? < ? 2 ? ? ? , ? < ? < 21