PTU B.Tech Petroleum Engineering 3rd Semester May 2019 72158 ENGINEERING MATHEMATICS III Question Papers

Roll No.

Total No. of Pages : 02

Total No. of Questions : 09

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B.Tech. (Petroleum Refinery Engineering) (2013 Onwards) (Sem.-3)

ENGINEERING MATHEMATICS-III

Subject Code : BTAM-201

M.Code: 72158

Time: 3 Hrs.

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Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

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SECTION-A

Write briefly :

1. Can f(x) = sin (1/x), - p = x = p be expanded in Fourier series?
2. Find the Laplace transform of f(t) = (sin t - cos t)².
3. Give the Laplace transform of Unit Impulse function.

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4. Find the Laplace inverse of 3 / (s² +6s+13)
5. Find the singular point of the differential equation Po (x) y" + P1 (x) y' + P2(x)y = 0.
6. Formulate the PDE from: z = ax + a²y² + b.
7. Solve the PDE: ?²z / (?x?y) = cos(2x+3y).
8. Find the poles of : f(z) = 1 / ((z-1)(z-2))

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9. Show that the function u = e? (x sin y - y cos x) is harmonic.
10. Find the residue of f(z) = (z²-2z) / (z²+4) at its poles.

SECTION-B

2. Find Fourier series expansion of f (x) = x², - p FirstRanker.com
3. 1. Evaluate L {e?²?t cos t}.

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   2. Find Laplace inverse of log ((1+s) / s)
4. Find the power series solution of the differential equation (1 – x²)y" – 2xy' + 2y = 0 about x = 0.
5. Solve the PDE: (x² - y² – z²) p + 2xyq = 2xz.
6. Find analytic function, whose real part is u=- (cos x) / (cosh 2 y-cos 2x)

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SECTION-C

7. 1. Using Laplace transform, solve y" + 2y' – 3y = sin t, given that y (0) = y'(0) = 0.
   2. Expand f (x) = x, 0 < x < p/2 and p-x, -p/2 < x < p as half range sine series.
8. 1. Solve the PDE: (mz – ny) p + (nx – lz) q = ly – mx.

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   2. Find the image of the line x = 2 in the z-plane.
9. Solve the equation ?u/?t = ?²u/?x² subject to the conditions u (x, 0) = 3 sin nx, u (0, t) = 0 and u (l,t) = 0, where 0 < x < l, t > 0.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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