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
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2141905 Date:22/11/2018
Subject Name:Complex Variables and Numerical Methods
Time: 02:30 PM TO 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Find the roots of the equation 03
(b) Show that is differentiable only at 04
(c) Solve the following system of equation by Gauss-Seidal method correct to
three decimal places.
07
Q.2 (a)
Evaluate along the line joining the points
03
(b) Determine the mobius transformation that maps
onto respectively.
04
(c) Prove that the roots of unity are in geometric progression. Also show
that their sum is zero.
07
OR
(c) Verify that C-R equation are satisfied at for the
function
07
Q.3 (a)
Evaluate
03
(b) Find the radius of convergence of
04
(c)
Using the residue theorem, evaluate
07
OR
Q.3 (a)
Expand as a Taylor?s series about the point
03
(b) Check whether is analytic or not. If analytic find its
derivative.
04
(c)
Evaluate counter clockwise around C, where C is
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2141905 Date:22/11/2018
Subject Name:Complex Variables and Numerical Methods
Time: 02:30 PM TO 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Find the roots of the equation 03
(b) Show that is differentiable only at 04
(c) Solve the following system of equation by Gauss-Seidal method correct to
three decimal places.
07
Q.2 (a)
Evaluate along the line joining the points
03
(b) Determine the mobius transformation that maps
onto respectively.
04
(c) Prove that the roots of unity are in geometric progression. Also show
that their sum is zero.
07
OR
(c) Verify that C-R equation are satisfied at for the
function
07
Q.3 (a)
Evaluate
03
(b) Find the radius of convergence of
04
(c)
Using the residue theorem, evaluate
07
OR
Q.3 (a)
Expand as a Taylor?s series about the point
03
(b) Check whether is analytic or not. If analytic find its
derivative.
04
(c)
Evaluate counter clockwise around C, where C is
07
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2
Q.4 (a) Using Newton?s forward formula , find the value of if
x 1 1.4 1.8 2.2
f(x) 3.49 4.82 5.96 6.5
03
(b) Find the Lagrange interpolating polynomial from the following data
x 0 1 4 5
f(x) 1 3 24 39
04
(c)
Find a root of +7 = 0 correct to three decimal places
between by Newton-Raphson method.
07
OR
Q.4 (a) Solve the system of equation by Gauss elimination method.
03
(b) Compute from the following values using Newton?s Divided
difference formula
x 4 5 7 10 11 13
f(x) 48 100 294 900 1210 2028
04
(c)
Evaluate taking and using Simpson?s rule. Hence
obtain approximate value of
07
Q.5 (a)
Evaluate
03
(b) Use power method to find the largest of Eigen values of the
matrix
04
(c) Use Euler?s method to obtain an approximate value of for the
differential equation
07
OR
Q.5 (a)
Prove that
03
(b)
Evaluate I = by one point, two point and three point
Gaussian formula.
04
(c) Determine correct upto four decimal places by fourth order
Runge-Kutta method from
07
*******
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This post was last modified on 20 February 2020