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ASSIGNMENT
DRIVE SPRING 2015
PROGRAM BCA(REVISED FALL 2012)
Semester 3
SUBJECT CODE & NAME BCA3010 - COMPUTER ORIENTED NUMERICAL METHODS
CREDIT 4
BK ID B 1643
MAX.MARKS 60
Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately
of 400 words. Each questionis followedbyevaluationscheme.
Q.1 Findthe Taylors Seriesfor (𝑥) = 𝑥3
− 10𝑥2
+ 6 about 𝑥0 = 3
Solution:Considerthe one dimensional initial value problem
y' = f(x,y), y(x0) = y0
where
f isa functionof twovariablesx andy and(x0 , y0) isa knownpointonthe solutioncurve.
Q. 2. Find a real root of the transcendental equation cos x – 3x+1 = 0, correct to four decimal places
usingiteration method.
Solution:IterationMethod:Letthe givenequationbe f(x) =0 and the value of x to be determined.By
usingthe Iteration methodyoucanfindthe roots of the equation.Tofindthe root of the equationfirst
we have to write equationlikebelow
x = pi(x)
Let x=x0be an initial approximationof the requiredrootα thenthe firstapproximationx1isgivenbyx1
= pi(x0).
Q.3 Solve the equations

2. 2x + 3y + z = 9
x + 2y + 3z = 6
3x + y + 2z = 8 by LU decompositionmethod.
Solution:We shall solve the system
2x + 3y + z = 9
x + 2y + 3z = 6
3x + y + 2z = 8
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:The givenstraightlinefitbe y= ax+b. The normal equationsof leastsqure fitare
axi2
+bxi =xiyi ---------------- (1)
and axi +nb = yi ---------------------(2)
Q.5 The populationof a certain town is shown inthe followingtable
Year X 1931 1941 1951 1961 1971
PopulationY 40.62 60.80 79.95 103.56 132.65
Findthe rate of growth of the populationin 1961.
Solution:
Year X 1931 1941 1951 1961 1971
PopulationY 40.62 60.80 79.95 103.56 132.65
Here h = 10
Q. 6. Solve of 𝑦 𝑛+2 −2 𝐶𝑜𝑠𝛼 𝑦 𝑛+1 + 𝑦 𝑛 = 𝐶𝑜𝑠 𝛼𝑛.
Solution:The order of the difference equationisthe difference betweenthe largestandsmallest
argumentsoccur-ringinthe difference equationdividedbythe unitof argument.Thus,the orderof the
difference equation=LargestargumentSmallestargumentUnitof argument.
We have yn = A2n
+ B(-2)n
=> yn-A2n
– B(-2)n

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