Alagappa University 2009 M.Arch Media history and laws in india pape - Question Paper

M.Sc. DEGREE EXAMINATION, MAY 2009.

Mathematics

DIFFERENTIAL EQUATION AND NUMERICAL METHODS

Time : Three hours Maximum : 100 marks

Answer any FIVE questions.

All questions carry equal marks.

1. (a) Prove that there exist linearly independent solution of on .

             (b) Find two linearly independent solutions of the equation .

2. Derive Bessel equation.

3. Deduce the methods of integrating the equations of the four standard forms of Charpits method.

4. (a) Find the integral surface of the linear partial differential equation .

             (b) Reduce the equation to canonical form.

5. (a) Find the multiple root of the equation using Newtons Method.

             (b) Obtain the least square polynomial approximation of degree 1 and 2 for = on .

6. (a) Derive uniform polynomial approximation.

             (b) Using Chebyshev polynomials obtain the least squares approximation of second degree for on .

7. Explain the Gauss-Hermite interpolation methods with examples.

8. (a) Solve the boundary value problem , with . Use Numerov Method in the interval .

             (b) Solve the boundary value problem :

             , , with use the second order method.