FirstRanker Logo

FirstRanker.com - FirstRanker's Choice is a hub of Question Papers & Study Materials for B-Tech, B.E, M-Tech, MCA, M.Sc, MBBS, BDS, MBA, B.Sc, Degree, B.Sc Nursing, B-Pharmacy, D-Pharmacy, MD, Medical, Dental, Engineering students. All services of FirstRanker.com are FREE

📱

Get the MBBS Question Bank Android App

Access previous years' papers, solved question papers, notes, and more on the go!

Install From Play Store

Download GTU B.Tech 2020 Winter 4th Sem 2141905 Complex Variables And Numerical Methods Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 4th Sem 2141905 Complex Variables And Numerical Methods Previous Question Paper

This post was last modified on 04 March 2021

This download link is referred from the post: GTU B.Tech 2020 Winter Question Papers || Gujarat Technological University


FirstRanker.com

GUJARAT TECHNOLOGICAL UNIVERSITY

BE- SEMESTER-IV (NEW) EXAMINATION - WINTER 2020

--- Content provided by FirstRanker.com ---

Subject Code:2141905 Date:09/02/2021

Subject Name:Complex Variables and Numerical Methods

Time:02:30 PM TO 04:30 PM Total Marks:47

Instructions:

  1. Attempt any THREE questions from Q.1 to Q.6.
  2. --- Content provided by FirstRanker.com ---

  3. Q.7 is compulsory.
  4. Make suitable assumptions wherever necessary.
  5. Figures to the right indicate full marks.

MARKS

Q.1 (a) Separate real and imaginary parts of f(z) = ez2, and also prove that it is analytic everywhere. 03

--- Content provided by FirstRanker.com ---

(b) Use De Moiver’s theorem and find 4th root of unity in the complex plane. 04

(c) Use Gauss-Jacobi method to determine roots of the following equations 07

20x+y—2z=17

3x + 20y —z=-18

2x — 3y + 20z =25

--- Content provided by FirstRanker.com ---

Q.2 (a) Evaluate the following integral along the curve 03

z(t) =t +it2

02+4i Re(z)dz

(b) Evaluate § (5z-2)/(z(z-1)) dz where C is the circle 04

  1. |z| =2
  2. --- Content provided by FirstRanker.com ---

  3. |z|=1/2

(c) Verify that u = x2 — y2+y is harmonic in the whole complex plane and finds it’s conjugate harmonic function v. 07

Q.3 (a) Obtain the Taylor’s series of f(z) = sin z in powers of (Z - π/2) 03

(b) Find the center and radius of convergence of the power series ∑n=0 (n+20)nzn. 04

(c) Find the Laurent’s series expansion of f(z) = 1/(z2-3z+2) in the region 07

--- Content provided by FirstRanker.com ---

  1. 1<|z|<2
  2. |z|>2

Q.4 (a) Find the Maclaurin’s series of f(z)=sin2z 03

(b) Find all values of z such that ez =1+ i 04

(c) Evaluate § (sinz)/(z2-4) dz counterclockwise around C: |z| = 5/2 07

--- Content provided by FirstRanker.com ---

Q.5 (a) Use Bisection method to find the real root of 03

x3 —4x —9 = 0. (Do 4 iterations)

(b) Using Newton’s divided difference interpolation formula, compute f(10.5) from the following data: 04

X 10 11 13 17
f(x) 2.3026 2.3979 2.5649 2.8332

(c) Evaluate ∫00.6 dx/(1+x) by Simpson’s 3/8 rule dividing into 6 intervals and hence calculate loge 2. Also, find the error involved in the process. 07

Q.6 (a) Approximate the root of the equation ex —2cosx =0, by three iterations of Newton Raphson method, taking initial approximation as X = 2. 03

--- Content provided by FirstRanker.com ---

(b) Find an approximate value of f(3.6) using Newton’s backward difference formula from the following data: 04

x 0 1 2 3 4
f(x) -5 1 9 25 55

(c) Using power method, determine the largest eigenvalue and the corresponding eigenvector of the matrix A = [[2, -1, 0], [-1, 2, -1], [0, -1, 2]], taking initial eigenvector x0 = [1, 0, 0]. 07

Q.7 Using three point Gaussian formula evaluate the following integral and compare with the exact value. 05

-11 dx/(1+ x2)

OR

--- Content provided by FirstRanker.com ---

Q.7 Solve the following system of linear equations using Gauss Elimination Method. 05

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

FirstRanker.com


--- Content provided by FirstRanker.com ---


This download link is referred from the post: GTU B.Tech 2020 Winter Question Papers || Gujarat Technological University