Download PTU B-Tech ECE 2020 Dec 3rd Sem 56071 Engineering Mathematics Iii Question Paper

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Roll No. Total No. of Pages : 02

Total No. of Questions : 18

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B.Tech. (CE)/(ECE)/(Electrical Engineering & Industrial Control)/ (Electronics & Computer Engg)/(Electronics & Electrical) (2012 to 2017)/ (Electrical & Electronics) (2011 Onwards)/(EE) (2012 Onwards)

(Sem.-3)

ENGINEERING MATHEMATICS - III

Subject Code : BTAM-301

M.Code : 56071

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Time : 3 Hrs. 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

Solve the following :

1. Find Laplace transform t * sin 3t.
2. Find inverse Laplace transform of 3s+23/(s+3).
3. Find inverse Laplace transform of e^-3s/(s+5).

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4. Using the value of F(x) = v(p/2x) ,show that J_½ (x) = v(2/px) sin x.
5. Express 3x² + 5x - 6 in terms of Legendre polynomials.
6. Derive a PDE by eliminating the arbitrary constants a and b from the equation x² + y² + (z -b)²=a².
7. Solve PDE (D²+DD'-2 D'²) z=0.
8. Show that the function f(z) = z does not have derivative at any point.

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9. If f(z) is an analytic function with constant modulus then f'(z) is constant.
10. State Cauchy’s Integral Formula.

SECTION-B

1. Find the Fourier series expansion of the function f(x) = x + p, -p < x < p. Hence show that p²/6 = 1 + 1/2² + 1/3² + 1/4² + ...
2. Find the solution of the initial value problem using the Laplace transform Y''+6y' +13y=e^-t,y(0)=0,y'(0)=4.

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3. Find two linearly independent solutions of the differential equation 2x²y" +xy' - (x²+ 1)y = 0, using Frobenius method.
4. Find the general solution of the partial differential equation (y +z)p+ (x +z) q=x+y.
5. Evaluate ?_c (z+1)/(z²(z-2)(z-4))dz, C:|z-3|=2.

SECTION-C

1. a) Write the Fourier cosine series of f(x) =
   

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   -1, 0<x<1
   1, 1<x<2
   b) Let f(t) be a piecewise continuous function on [0, 8), be of exponential order and periodic with period T. Then L [ f (t)] = 1/(1-e^-sT) ?₀^T e^-st f(t)dt.
2. a) State and Prove Rodrigue's Formula.
   b) Using the method of separation of variables, solve ?u/?x = 2?u/?y +u,u(x,0) = 6e^-3x

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3. Find all Taylor and Laurent series expansions of f(z) = 1/((z+1)(z+2)) about the point z=1.

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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