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Sma2109:Applied Mathematics Question Paper

Sma2109:Applied Mathematics

Course:Bachelor Of Computer Science

Institution: Meru University Of Science And Technology question papers

Exam Year:2013

QUESTION ONE (30 MARKS)
a) i) Find the sum of the series below using Euler-Maclaurin formula 1 512 + 1 532 + 1 552 + ?+ 1 992 (3 Marks) ii) Evaluate ??-??2 0.4 0.2 (4 Marks) b) Express ?? = 3??4 + ??2 + ?? + 1 in factorial functions and hence show that ?3?? = 18. (5 Marks) c) Find the Lagrange form of the interpolating polynomial that fits the following data, hence find ??(1 2 ). ?? 1 3 1 4 1 ??(??) 2 -1 7 (7 Marks) d) Using Newton-Raphson, evaluate to 3 decimal places 12. (3 Marks) e) Using the iteration formula ????+1 = 4 - 1 ???? , find to 2d.p a root of the equation ??2 - 4?? + 1 = 0. Starting with ??0 = 3. (4 Marks) f) cos?? upto the term in ??4 with ??0 = 0 and find the appropriate value of cos0.5. (4 Marks)
QUESTION TWO (20 MARKS) a) cos ?? 3 + h in ascending power of upto h6. Taking 3 = 1.7321 ?????? 5.5° as 0.09599 radians, find the value of cos54.5° to 4 decimal places. (8 Marks)
2
b) The following values of the function ?? ?? = sin?? + cos?? are given ?? 10° 20° 30° ??(??) 1.585 1.2817 1.3660
Construct the quadratic interpolating polynomial that fits the data, hence find ?? ?? 12 . (6 Marks) c) interpolation formula, find the value of y(10) from the following data x 5 6 9 11 y 12 13 14 16 (6 Marks)
QUESTION THREE (20 MARKS)
a) The values for ?? ?? = ?????? are given in the table below x F(x) 2.0 0.69315 2.2 0.78846 2.6 0.95551 Find the approximate value of i. ??'(2.0) using linear interpolation (4 Marks) ii. ??"(2.0) using quadratic interpolation (6 Marks) b) Using the forward difference formula, find the first and second derivatives of ?? at x = 15 from the table below ?? 15 17 19 21 23 ?? 3.873 4.123 4.359 4.583 4.796 (10 Marks)
QUESTION FOUR (20 MARKS)
a) Find a root of the equation 2??3 - 2?? = 8 lying between 1 and 3, to 3 decimal places using i. Newton – Raphson method. (7 Marks) ii. Method of False position. (13 Marks)
QUESTION FIVE (20 MARKS)
a) Using Euler- log?? 2 from ???? 1+?? 2 1 0
. (7 Marks) b) 1 3 rule, find ???? 1+?? 2 6 0 . (6 Marks) c) 3 8 rule is
??(??) ??0+??h ??0
???? = 3 8 h ??0 + ???? + 3 ??1 + ??2 + ?+ ????-2 + ????-1 + 2 ??3 + ??6 + ?+ ????-3 (7 Marks)

Sma2109:Applied Mathematics Question Paper

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