Download GTU BE/B.Tech 2019 Summer 3rd Sem Old 130002 Advanced Engineering Mathematics Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 3rd Sem Old 130002 Advanced Engineering Mathematics Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III(OLD) EXAMINATION ? SUMMER 2019
Subject Code: 130002 Date: 30/05/2019

Subject Name: Advanced Engineering Mathematics

Time: 02:30 PM TO 05:30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 (a) (i) Solve
(ii) Solve y?- ( 1 + 3 x
-1
)y = x+2; y(1) = e ?1
03
04

(b) Find the Power series solution of the differential equation y?? = y?. 07

Q.2 (a) Using the method of separation of variables solve uxx = 16 u y. 07
(b) Find the series solution of the differential equation by Frobenius method

07
OR
(b) (i) Solve y?? + 4y = 8 cos2x, y(0) = 0, y?(0) = 2
(ii) Solve y??- 4y? - 12y = 7 e
?7x
by method of undetermined coefficients.
03
04

Q.3 (a) Find the Fourier series for the function f(x) = x
2
+ x, - ? ? x ? ?.

07
(b) Find the Fourier series of the function


07

OR

Q.3 (a) Find the Fourier series with period 3 to represent f(x) = 2x ? x
2
in the range
(0, 3).
07
(b) Find the half range Fourier cosine series of the function f(x) = c ? x in interval
(0, c) with period 2c.
07

Q.4 (a) (i) Find the Laplace transform of e
? t
(4t
3
+ 3cos2t + 2e
?2t
)
(ii) Prove that

s > 0, where is a constant.
03
04
(b) Find the Inverse Laplace transform of

07

OR

Q.4 (a) (i) Find the Laplace transform of

(ii) Find the Inverse Laplace transform of

03



04
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III(OLD) EXAMINATION ? SUMMER 2019
Subject Code: 130002 Date: 30/05/2019

Subject Name: Advanced Engineering Mathematics

Time: 02:30 PM TO 05:30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 (a) (i) Solve
(ii) Solve y?- ( 1 + 3 x
-1
)y = x+2; y(1) = e ?1
03
04

(b) Find the Power series solution of the differential equation y?? = y?. 07

Q.2 (a) Using the method of separation of variables solve uxx = 16 u y. 07
(b) Find the series solution of the differential equation by Frobenius method

07
OR
(b) (i) Solve y?? + 4y = 8 cos2x, y(0) = 0, y?(0) = 2
(ii) Solve y??- 4y? - 12y = 7 e
?7x
by method of undetermined coefficients.
03
04

Q.3 (a) Find the Fourier series for the function f(x) = x
2
+ x, - ? ? x ? ?.

07
(b) Find the Fourier series of the function


07

OR

Q.3 (a) Find the Fourier series with period 3 to represent f(x) = 2x ? x
2
in the range
(0, 3).
07
(b) Find the half range Fourier cosine series of the function f(x) = c ? x in interval
(0, c) with period 2c.
07

Q.4 (a) (i) Find the Laplace transform of e
? t
(4t
3
+ 3cos2t + 2e
?2t
)
(ii) Prove that

s > 0, where is a constant.
03
04
(b) Find the Inverse Laplace transform of

07

OR

Q.4 (a) (i) Find the Laplace transform of

(ii) Find the Inverse Laplace transform of

03



04
2
(b) Using Laplace transform solve the differential equation y?? + 6y = 1, y(0) = 2,
y?(0) = 0
07

Q.5 (a) (i) Form Partial differential equation by eliminating the arbitrary function from
the equation

(ii) Define the following: (1) Beta function (2) Dirac?s Delta Function
03



04
(b) Express the function as a Fourier Integral

07
OR

Q.5 (a) (i) Solve : p + q = pq
(ii) Solve: x (y
2
?z
2
) p + y (z
2
? x
2
) q = z(x
2
? y
2
).
03
04
(b) Solve the following:

(ii) (D ? D? - 1) (D - D? -2) z = e
2x ? y



07


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