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Spring
2015, ASS IGNMENT
PROGRAM BCA (REVISED FALL 2012)
SEMESTER 3
SUBJECT CODE &
NAME
BCA3010 -COMPUTER ORIENTED NUMERICAL
METHODS
CREDIT 4
BK ID
B1643
Q.1. Find the Taylors
Series for f(x)=x3-10x2+6 about x0=3
Solution.
We
know that Taylor's series expansion of function at
Q.2. Find a real root of the
transcendental equation cos x-3x+1=0,
correct to four decimal places using iteration method.
Solution.
Let f(x) = cos x – 3x + 1.
Now f(0) = cos 0 – 0 + 1 = 2 > 0 and
Q.3. Solve the equations
2x + 3y + z = 9
x + 2y + 3z = 6
3x + y + 2z = 8
by LU decomposition method.
Solution.
Q.4. Fit a second degree
parabola y = a + bx + cx2
in the least square method for the following data and hence estimate y
at x = 6.
X
|
1
|
2
|
3
|
4
|
5
|
Y
|
10
|
12
|
13
|
16
|
19
|
Solution.
Let
us choose, X=x-3, we have y'= (∑y)/n =70/5=14
and let
Y = y – y' =
Q.5. The population of a certain town is
shown in the following table
Year X
|
1931
|
1941
|
1951
|
1961
|
1971
|
Population Y
|
40.62
|
60.80
|
79.95
|
103.56
|
132.65
|
Find the rate of growth of the
population in 1961.
Solution.
Here h = 10. Since the rate of growth of population is
dy/dx, we have to find dy/dx at x= 1961, which lies nearer to the end value of
the table.
Hence we choose the
Q.6. Solve of π¦π+2- 2 πΆππ πΌ π¦π+1+ π¦π= πΆππ πΌπ.
Solution.
The given difference
equation can be written as
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