Tamil Nadu Open University (TNOU) 2009-1st Year M.Sc Mathematics Tamilnadu open university Maths Numerical methods and differential equation - Question Paper
M.Sc. DEGREE exam – JUNE 2009.
(AY 2005–06 and CY 2006 batches only)
First Year
NUMERICAL METHODS AND DIFFERENTIAL EQUATIONS
Time : three hours Maximum marks : 75
PART A — (5 x five = 25 marks)
ans any 5 ques..
1.Derive iteration formula to calculate using Newton’s method. Hence calculate , corrected to six decimal places.
2.Solve the system of equations
, Using Gauss – Jordan method.
3.Calculate the divided difference of .
4.Evaluate , using Gauss–Legendre three pt. formula.
5.Show that the differential formula has solution of the form is a constant.
6.Find singular points of and classify the identical.
7.Solve the differential formula .
8.Find the complete integral of .
PART B — (5 x 10 = 50 marks)
ans any 5 ques..
9.By Tricurgularization method, solve the system of equations.
10.Find inverse of the matrix by the partition method.
11.Find approximate value of the integral using composite Simpson’s rule with 3,5 and
9 nodes and Romberg integration.
12.Solve the initial value issue with on the interval
[0, 0.4], using 2nd order implicit Runge–Kutta method.
13.Find 2 linearly independent power series solutions of the formula .
14.Prove that Bessel function of order of 1st type is provided by .
15.Show that a function is a solution of initial value issue on an interval I iff it’s a solution of integral formula
on I.
16.Find the surface orthogonal to 1 parameters system and which passes through the hyperbola .
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M.Sc. DEGREE EXAMINATION JUNE 2009.
(AY 200506 and CY 2006 batches only)
First Year
NUMERICAL METHODS AND DIFFERENTIAL EQUATIONS
Time : 3 hours Maximum marks : 75
PART A (5 5 = 25 marks)
Answer any FIVE questions.
1.
Derive iteration formula to compute 
using
Newtons method. Hence compute 
, corrected
to 6 decimal places.
2.
Solve the system of equations 
, Using Gauss Jordan method.
3.
Calculate the 
divided difference
of 
.
4.
Evaluate 
, using
GaussLegendre 3 pt. formula.
5.
Show that the differential equation 
has
solution of the form 
is a constant.
6.
Find singular points of 
and
classify the same.
7.
Solve the differential equation 
.
8.
Find the complete integral of 
.
PART B (5 10 = 50 marks)
Answer any FIVE questions.
9. By Tricurgularization method, solve the system of equations
.
10. Find inverse of the matrix
by
the partition method.
11. Find
approximate value of the integral 
using
composite Simpsons rule with 3,5 and
9 nodes and Romberg integration.
12. Solve the initial value problem
with
on the interval
[0, 0.4], using second order implicit RungeKutta method.
13. Find two linearly independent power series solutions of the equation
.
14. Prove
that Bessel function of order 
of first
kind is given by 
.
15. Show
that a function 
is a solution of
initial value problem 
on an interval I
iff its a solution of integral equation 
on I.
16. Find
the surface orthogonal to one parameters system 
and
which passes through the hyperbola 
.
| Earning: Approval pending. |
