Annamalai University 2008-3rd Year B.Sc Mathematics " 720 NUMERICAL METHODS AND TRIGONOMETRY " ( PART - III - A - MAIN ) ( ) ( - V ) 5237 - Question Paper
4
(b) Use Graeffes method to solve the equation
3 2 0
x - x - x = 2.
6. (a) Solve, by Gauss - Seidal method of
iteration, the equations
27x + 6y - z = 85
6x + 15y + 2z = 72
x + y + 54z = 110.
(b) Using Taylor series method, compute the value of y(0-2) correct to 3 decimal places from
dy
= i - 2xy, dx
given that y(0) = 0.
7. (a) Use Eulers method to find y(0-4) given
dy
= xy, y(0) = 1.
dx
(b) Apply the fourth order Runge - Kutta method to find y(0-2) given that
dy
-2- = x + y, y(0) = 1. dx
Name of the Candidate :
5 2 3 7 B.Sc. DEGREE EXAMINATION, 2008
(MATHEMATICS)
(THIRD YEAR)
(PART - III - A - MAIN)
(PAPER - V)
720. NUMERICAL METHODS AND TRIGONOMETRY
(Including Lateral Entry )
December ] [ Time : 3 Hours
Maximum : 100 Marks
Answer any FIVE questions.
All questions carry equal marks.
(5 x 20 = 100)
1. (a) The following table indicates the values taken from a record. Find the value of y at x = 1-05, using Newtons forward interpolation formula:
|
x: |
1-0 |
1-1 |
1-2 |
1-3 |
1-4 |
1-5 |
|
y: |
0-841 |
0-891 |
0-932 |
0-964 |
0-985 |
1-015 |
(b) From the given table, compute the value of sin 38 :
|
X |
0 |
10 |
20 |
30 |
40 |
|
sin x |
0 |
0-17365 |
0-34202 |
0-5000 |
0-64279 |
2. (a) Using Stirlings formula, compute y(35) from the data given below :
|
x: |
20 |
30 |
40 |
50 |
|
y: |
512 |
439 |
346 |
243 |
(b) Construct Newtons forward interpolation polynomial for the following data. Use it to find the value of y for x = 5.
|
x: |
4 |
6 |
8 |
10 |
|
y: |
1 |
3 |
8 |
16 |
3. (a) Given the following data:
|
x: |
0 |
1 |
2 |
3 |
4 |
|
y: |
1 |
1 |
15 |
40 |
85 |
using
(i) Trapezoidal rule.
(ii) Simpsons one third rule by taking
h = -L .
6
Solve the equation
4. (a)
x4 - x - 9 = 0
for roots lying between 1 and 2 by Newton Raphson method.
(b) Use Regula - Falsi method to find the real root of xex -3 = 0, correct to three decimal places.
5. (a) Find a real root of the equation
cos x = 3x - 1
correct to 3 decimal places by using iteration method.
-l -l -l ft tan x + tan y + tan z = ,
show that
xy + yz + zx = 1.
(b) If n is a positive integer, prove that (1 +i) + (1 _i)n = ({2)n + 2 n71
cos
2 '
9. (a) Solve:
x9 + x5 - x4 - 1 = 0.
(b) Show that the product of the four values of
>3/4
71 . . 7t \
cos + 1 sin - ; i
3 3 ) 1S x-
10. (a) Show that
4n + 1
log. i =
4m + 1 where m and n are integers.
(b) Show to n terms of the series
sin a + sin (a + (3) + sin (a + 2(3) +
-l -l -l ft tan x + tan y + tan z = ,
show that
xy + yz + zx = 1.
(b) If n is a positive integer, prove that
(1 + ,) + (l-,) = (-fi )n + 2 C0SI!
9. (a) Solve:
x9 + x5 - x4 - 1 = 0.
(b) Show that the product of the four values of
>3/4
71 . . 7t \
cos + 1 sin - ; i
3 3 / 1S x-
10. (a) Show that
4n + 1
log. i =
4m + 1 where m and n are integers.
(b) Show to n terms of the series
sin a + sin (a+(3) + sin (a + 2(3) +
|
Attachment: |
| Earning: Approval pending. |
