# Loyola College B.Sc. Mathematics April 2009 Numerical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

 ZA 38

SIXTH SEMESTER – April 2009

# MT 6605 – NUMERICAL METHODS

Date & Time: 23/04/2009 / 9:00 – 12:00 Dept. No.                                                     Max. : 100 Marks

PART – A (10 ´ 2 = 20)

1. What do you mean by partial pivoting?
2. State Cramer’s rule.
3. What is the order of convergence in Newton-Raphson method?
4. Explain bisection method.
5. What is meant by interpolation?
6. Write the error polynomial in the Newton’s forward interpolation formula?
7. Write the Stirling’s central difference interpolation formula.
8. Write any two advantages of central difference interpolation formula.
9. What is the order of error in the Trapezoidal rule?
10. Write the formula for third order Range-Kutta method.

PART – B (5 ´ 8 = 40)

1. Solve the following system of equations by Gauss elimination method

28x + 4y – z = 32,       x + 3y + 10z = 24    and     2x + 17y +4z = 35.

1. Solve for a positive root of x3 – 4x + 1 = 0 by Regula Falsi method.
2. Write a C program to for Lagrange’s interpolation formula.
3. Obtain Newton’s forward interpolation formula for equal intervals.
4. Find the first two derivatives of at x = 50 and x = 56 given the table below:

x                        :              50            51              52          53           54           55             56

:           3.6840     3.7084      3.7325    3.7563   3.7798     3.8030      3.8259

1. Use Laplace-Everett’s formula to obtain f(1.15) given that f(1) = 1, f(1.1) =1.049,  f(1.2) = 1.096, f(1.3) = 1.14.
2. Evaluate by        (i) Trapezoidal rule      (ii) Simpson’s 1/3  rule   and

(iii) Simpson’s 3/8 rule.

1. Solve in the range 0 £ x £2 using (i) Euler’s method  (ii) improved Euler’s method

PART – C (2 ´ 20 = 40)

1. (a) Solve by Gauss-Seidel Method, the following system of equations.

28x + 4y – z = 32,

x + 3y + 10z = 24,

and      2x + 17y + 4z = 35

(b) Find the real positive root of 3x – cos x – 1 = 0 by Newton-Raphson method correct to 6 decimal places.

1. (a) From the following table find f(x) and hence f(6) using Newton’s divided difference formula.

x          :           1             2            7             8

f(x)       :           1             5            5             4

• The following table gives the value of density of saturated water for various temperatures of saturated stream.

Tempo C ( = T)            :           100      150      200      250      300

Density hg/m3 (= d)     :           958      917      865      799      712

Find by interpolation, the densities when the temperatures are 130oC and 275oC respectively.

1. (a) Using Gauss’s forward interpolation formula, find the value of log 337.5 from the following table.

x                 :              310           320            330            340          350          360

yx = log x        :           2.4914       2.5052       2.5185      2.5315      2.5441   2.5563

• Using Bessel’s formula, find the derivative of f(x) at x = 3.5 from the following table.

x          :           3.47     3.48     3.49     3.50     3.51     3.52     3.53

f(x)       :           0.193   0.195   0.198   0.201   0.203   0.206   0.208

1. (a) Using Range-Kutta method of fourth order, solve for y(0.1) and y(0.2) given that                 y¢ = xy + y2, y(0) =1.

(b)  Develop a C program to implement Simpson’s 3/8 rule.

Go To Main page

Latest Govt Job & Exam Updates:

# View Full List ...

© Copyright Entrance India - Engineering and Medical Entrance Exams in India | Website Maintained by Firewall Firm - IT Monteur