## Question Paper of ADVANCED MATHEMATICS FOR ENGINEERS for M.Tech (PE) (Sem.- 1st), SUBJECT CODE : EC-501, Paper ID [ E0442 ], PTU Question Paper.

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Roll No……….
Total No. of Questions: 08

M. Tech. (Sem.-1st)
SUBJECT CODE : EC-501
Paper ID: [E0561]

Time: 03 Hours                                                   Maximum Marks: 100
Instruction to Candidates:
1.     Attempt any Five questions.
2.     All questions carry equal marks.

Q1) Find the Fourier sine transform of . Hence evaluate Q2)  State and prove the Convolution theorem for Fourier transforms.

Q3) Find the Z –transform of sin (3k+5).

Q4) Solve the following system of equations,
2 +3 +4 =20
4 +2 +3 =17 +4 +2 =17
Using Gauss elimination method.

Q5) It is possible to solve the following equations by Crout’s method. If so,  solve them.
10x+y+z=12, 2x+10y+z=13, 2x+2y+10z=14.

Q6)  Find the transformation which maps the points 1, -I, 1 of the z-plane or onto 0,1, , of the w-plane respectively.

Q7) State and prove the Hamilton’s principle.

Q8) A smooth curve in the xy-plane of fixed length 1 passes through the points (-a, 0) and (a, 0).  Determine the curve if the area bounded by the curve and the x-axis is a maximum.