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Download GTU BE/B.Tech 2018 Winter 4th Sem New 2141905 Complex Variables And Numerical Methods Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 4th Sem New 2141905 Complex Variables And Numerical Methods Previous Question Paper

This post was last modified on 20 February 2020

This download link is referred from the post: GTU BE/B.Tech 2018 Winter Question Papers || Gujarat Technological University


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Seat No.:

GUJARAT TECHNOLOGICAL UNIVERSITY

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BE - SEMESTER-1V (NEW) EXAMINATION - WINTER 2018

Subject Code:2141905

Subject Name:Complex Variables and Numerical Methods

Time: 02:30 PM TO 05:30 PM

Instructions:

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  1. Attempt all questions.
  2. Make suitable assumptions wherever necessary.
  3. Figures to the right indicate full marks.

Q1

  1. (a) Find the roots of the equation Z2 + 2iz + (2—4i)=0 [03]
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  3. (b) Show that f(z) = z Re(z) is differentiable only at z = 0 and f'(0) = 0. [04]
  4. (c) Solve the following system of equation by Gauss-Seidal method correct to three decimal places. [07]
    2x + y + 54z = 110
    27x + 6y — z = 285
    6x + 15y + 2z = 72
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Q2

  1. (a) Evaluate ∫c (2+i) z2 dz along the line joining the points(0,0)and (2,1). [03]
  2. (b) Determine the mobius transformation that maps z1 =0, z2 =1, z3 = ∞ onto w1 = —1, w2 = —i, w3 = 1 respectively. [04]
  3. (c) Prove that the nth roots of unity are in geometric progression. Also show that their sum is zero. [07]
    OR
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  5. (c) Verify that C-R equation are satisfied at z=0 for the function
    f (z) = { z2 / z̄ if z≠0
    0 if z=0

Q3

  1. (a) Evaluate ∫c [z3 / (z—6i)2] dz, where C: |z| = 2. [03]
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  3. (b) Find the radius of convergence of ∑ (2n+5) / (2n) (z+2i)n [04]
  4. (c) Using the residue theorem, evaluate ∫0 dθ / (5-3sinθ) [07]
    OR
  5. (c) Expand f (z) = (z-1) / (z2+3z+2) in a Taylor’s series about the point z = 0. [07]

Q3

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  1. (a) Check whether f(z) = sinz is analytic or not. If analytic find its derivative. [03]
  2. (b) Evaluate ∫c (z2—z+z-1) / (z2-z) dz counter clockwise around C, where C is |z| =1 and |z| = 3. [04]

Date:22/11/2018

Total Marks: 70

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Q4

  1. (a) Using Newton’s forward formula , find the value of f(1.6) if [03]
    X 1 1.4 1.8 2.2
    f(x) 3.49 4.82 5.96 6.5
  2. (b) Find the Lagrange interpolating polynomial from the following data [04]

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    X 0 1 4 5
    f(x) 1 3 24 39
  3. (c) Find a root of x4 — x3 + 10x+7 = 0 correct to three decimal places between a = —2 and b = —1 by Newton-Raphson method. [07]
    OR
  4. (c) Solve the system of equation by Gauss elimination method. [07]

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    x+y+z=9
    2x—3y+4z=13
    3x+4y+5z=40

Q.5

  1. (a) Compute f(8) from the following values using Newton’s Divided difference formula [03]

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    X 4 5 7 10 11 13
    f(x) 48 100 294 900 1210 2028
  2. (b) Evaluate ∫61 1/(1+x) dx ,taking h =1 and using Simpson’s 1/3 rule. Hence obtain approximate value of log 7. [04]
  3. (c) Use power method to find the largest of Eigen values of the matrix A = [[4, 2], [1, 3]] [07]
    OR
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  5. (c) Use Euler’s method to obtain an approximate value of y(0.4) for the differential equation y’ = x +y, y(0) = 1 with h=0.1. [07]

Q.5

  1. (a) Prove that kD = log(1 + Δ) [03]
  2. (b) Evaluate I = ∫-11 1/(1+x2) dx by one point, two point and three point Gaussian formula. [04]
  3. (c) Determine y(0.1), y(0.2) correct upto four decimal places by fourth order Runge-Kutta method from dy/dx =2x+y, y(0)=1 [07]
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This download link is referred from the post: GTU BE/B.Tech 2018 Winter Question Papers || Gujarat Technological University

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