LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2012

PH 3812 – NUMERICAL METHODS AND C PROGRAMMING

 

 

Date : 06/11/2012            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL questions:                                                                                                               (10×2=20)

 

1. Describe the structure of a C program.
2. Distinguish between main() and void main(void).
3. Write a C program to output the multiplication table.
4. Check whether the following numeric constants are valid. Give reason.
5. a) 67845L b) 25,000        c) +5.0E3        d) 7.1e 4          e) $ 285
6. How do variables and symbolic names differ?
7. Develop a C program to convert lowercase letter to upper case and vice-versa.
8. Apply Simpson’s 1/3 ^rd rule to estimate the value of the integral by dividing the interval (1,2) into four equal parts.
9. Given that f(0)=8, f(1)=68 and f(5)=123 ,construct a divided difference table. Using the table determine the value of f(2).
10. Differentiate between break and continue statements.
11. Briefly explain the various data types in C language.

PART – B

Answer any FOUR questions            :                                                                                                    (4×7.5=30)

11. Using Newton’s formula for interpolation with x and y given values and find f(7.5) for the data given below.

X	1	2	3	4	5	6	7	8
F(x)	1	8	27	64	125	216	343	512

12. Using Newton-Raphson’s method find correct to four decimal places, the roots lying in the interval 0 and 1 for the equation x³-6x+4=0.
13. Write a C program to evaluate the sum of the digits of a given number.

14 Determine y by Lagrange’s formula when x=35, for the data given below.

x	25	30	40	50
y	52	67.3	84.1	94.4

15. Write a C program to perform integration of a function using Trapezoidal rule.

PART – C

Answer any FOUR questions            :                                                                                                   (4×12.5=50)

16. Given that dy/dx=1+y², where y=0, when x=0, Find y(0.2) and y(0.4) by using Runge-Kutta method of order four.
17. Develop a C program to find the transpose of a matrix.
18. Find the value of y for x=0.2 when dy/dx=log(x+y) with the initial condition that y=1 for x=0 by using Euler’s modified method.
19. Solve the following simultaneous equations by Gauss-Jordan method

x₁+2x₂+x₃=8;                    2x₁+3x₂+4x₃=20;                     4x₁+3x₂+2x₃=16.

20. i) Discuss the various storage classes in C with suitable examples.
21. ii) Write a C program to accept a sequence of characters and find the number of vowels and consonants using switch statement.

 

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