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Sma2110:Real Analysis Ii Question Paper

Sma2110:Real Analysis Ii

Course:Bachelor Of Computer Science

Institution: Meru University Of Science And Technology question papers

Exam Year:2010

QUESTION ONE (30 MARKS)
(a) Using Garssian elimination method, solve the following system of Linear equations 1:1 + 2 + 23 4 = 8 2: 21 22 + 33 34 = 20 3:1 + 2 + 3 = 2 4:1 2 + 43 + 34 = 4 (8 Marks)
(b) corresponding to = 2 given that = + 2 = 1 = 1 . (6 Marks)
(c) Evaluate dx x ex 1 0
(4 Marks)
(d) Values for = are given in the table below
x f(x) 1.8 10.889365 1.9 12.703199 2.0 14.778112 2.1 17.148957 2.2 19.855030
2
Approximate 2.0 using the Three-point formula also find the exact value of (2.0) (5 Marks) (e) Obtain the least square straight line fit to the following data. (7 Marks)
QUESTION TWO (20 MARKS)
(a) Solve the + 2 + = 4, 2 3 = 3, 3 + + 2 = 3 (7 Marks)
(b) With the following system of equations 3 + 2 = 4.5 2 + 3 = 5 + 2 = 0.5
Set up the Gauss-seidel iteration scheme for solution. Iterate two times using the initial approximation as 0 = 0.4, 0 = 1.6, 0 = 0.4. (6 Marks)
(c) Find the least square approximation of the second degree for the discrete data
(7 Marks) QUESTION THREE (20 MARKS)
(a) Find the solution (0.1) of the initial value problem = 22, 0 = 1 with = 0.1, using (i) Taylor series method of order four. (6 Marks) (ii) Runge-Kutta method of order four. (8 Marks)
(b) . = 2 + 1, 0 2, 0 = 0.5 with = 0.5 (6 Marks)
x 0.2 0.4 0.6 0.8 y 0.477 0.632 0.775 0.894
x -2 -1 0 1 2 f (x) 15 1 1 3 19
3
QUESTION FOUR (20 MARKS)
(a) 2 2 2 2 2 2 8 y x y u x u
for the square mesh of the figure given
below with , = 0 on the boundary and mesh = 1 (8 Marks)
u1 u2 u1 u1 u3 u2 u1 u2 u1
(b) Solve 2 2 2 2 x u t u
with conditions 0, = 1, = 0, ,0 = 1 2
(1 ) and
,0 = 0, taking = = 0.1 0 0.4. (12 Marks)
QUESTION FIVE (20 MARKS)
(a) Given the following values of () () x f(x) f´(x) -1 1 -5 0 1 1 1 3 7
Estimate the values of (0.5) and (0.5) using the Hermite interpolation. (15 Marks) (b) Compute by using Taylor development. (5 Mark

Sma2110:Real Analysis Ii Question Paper

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