National Institute of Technology, Delhi
Name of the Examination: B.Tech.
Mid Semester Examination (Spring, 2021)
Branch
:ECE/EEE
Semester
: 4th
Title of the Course
: PDE and Numerical Analysis
Course Code
: MAL-251
Time
: 1.5 Hours
Max. Marks
: 25
_____________________________________________________________________________
Note: Attempt all questions. Marks for each question are indicated against it.
1.
Use Newton-Raphson method to determine the at least two positive root of
f=
( x) log x + sin x upto 4 decimal of places.
[4]
2.
Find the rate of convergence for the Linear Interpolation Method.
3.
Given below the values of f ( x) tabulated for
[3]
x
1.00
1.20
1.40
1.60
1.80
2.00
f ( x)
2.7183
3.3201
4.0552
4.9530
6.0496
7.3891
Find f (1.68) using Newton’s backward difference method.
4.
[4]
Following values of the function y = x3 are provided,
x
1
2
3
y
1
8
27
Compute cube-root of 21 from the above data using Lagrange’s method.
[4]
1.2
5.
Evaluate the integral I =
−x
∫ e dx by (i) Trapezium rule (ii) Simpson’s 1/3 rule. Take
2
0
h = 0.2 . Also estimate the error in the composite trapezium.
6.
[6]
Find numerical differentiation for f '(3), f ''(3) from the following table
x
3
3.2
3.4
3.6
3.8
4
f ( x)
-14
-10.032
-5.296
-0.256
6.672
14
[4]
End of the Question Paper
Page 1 of 1