bca3010 smu bca spring 2017 (jul/aug 2017 exam) IIIrd sem assignment

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Spring 2017 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 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

 

.2. Find the Taylors Series for f(x)=x³-10x²+6 about x₀=3

Solution.

We know that Taylor's series expansion of function at point x₀ is

Q.3. Solve the equations

2x + 3y + z = 9

x + 2y + 3z = 6

3x + y + 2z = 8

by LU decomposition method.

Solution.

  We have,

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

Q.6. Solve of 𝑦_𝑛+2- 2 𝐶𝑜𝑠 𝛼 𝑦_𝑛+1+ 𝑦_𝑛= 𝐶𝑜𝑠 𝛼𝑛.

Solution.

The given difference equation can be written as

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