M.Sc. (Semester (CBCS) Examination Mar/Apr-2018
Electronics
NUMERICAL METHODS
Time: 2½ hrs
Max. Marks: 70
Instructions: Q. and are compulsory. Answer any three questions from Q.3 to Q.7. Answer five questions. Figures to the right indicate full marks.
Q.1
Choose the alternatives given below.
08
Laplace transform converts the function of
frequency domain into time domain
time domain into frequency domain
time domain into continuous time domain
None of these
To obtain solution of system of linear equations, the coefficient matrix should be
Singular
Unity
Non-singular
All of these
Laplace Transform of tn is given by
1/S



Newton's Cotes integration formula for four points reduce to
Simpson 1/3 rule
Trapezoidal rule
Simpson 3/8 rule
All of these
Transpose of co-factor matrix is
adjoint matrix
inverse matrix
sparse matrix
All of these
For Newton's forward method of interpolation the u is given by
u
u
u
u
The divided difference method is used for the data points of
equal interval
unequal interval
negative interval
positive interval
For R-K second order method are Taylor's series can be truncated from
Oh2
Oh3
Oh4
Oh5
State True or false.
06
Interpolation is the process of getting empirical expression from given data.
Numerical integration for two variables is called quadrature.
Laplace transformation of sinwt 1 (s2 w2)
Lagrangian method is used for interpolation of unequal spacing data points.
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SLR-UJ-321
Expression for getting numerical solution of first order ordinary differential equation is derived from Taylor series.
In Guass Jordon elimination method the coefficient matrix should be reduced to upper triangular matrix.
Q.2
Attempt any two.
10
Derive expression for Laplace transformation of sinwt.
Using least squares fitting process, fit following data to straight line.
Solve
x1 x2 2x3 4 3x1 x2 3x3 2x1 3x2 5x3
What do you mean by pivoting?
04
Q.3
What do you mean by Newton's Cotes Integration formula? Derive expression for Simpson's mid-point and one third rule for numerical integration.
08
Evaluate by using Simpson's one third method.
06
Q.4
What do you mean numerical differentiation? Derive expression for Newton's forward difference formula for numerical differentiation.
08
Find first and second order derivatives at x 2.0 for following data point
06
Q.5
What do you mean by Laplace Transformation of the given function? Describe in detail the analysis of RC circuit by using Laplace Transformation.
08
Evaluate by using composite trapezoidal rule for 10 intervals.
06
Q.6
Describe formation of system of linear equations? Describe Gaussian elimination method for solution of system of linear equations.
08
Using Newton's forward difference interpolation method generates interpolating polynomial for following data points.
06
Q.7
Describe R-K methods of finding solution of first order ordinary differential equation.
08
Using RK II order method find value of y(0.2) Given that
dydx=1−y 2 and y 0