M.Sc. (Physics)

Computational Methods and Programming

Semester:-4^th

Year: - June 2010

Maximum marks:-35

Minimum marks:-12

 

Section A

Choose correct answer from following questions. Each having marks each.

 

 

1. Each C program should contain a function known as:-

(i) File handling function

(ii) Main function

(iii) Other function

(iv) None of these.

 

2. Identify which of the following word in C is key word:-

(i) bit

(ii) end

(iii) else

(iv) Define.

 

3. The storage space required for character data type is:-

(i) 1 byte

(ii) 2 byte

(iii) 4 byte

(iv) 8 byte.

 

 

 

4. The procedure for passing the value of a given argument to a function is known as:-

(i)Static variable

(ii)Register variable

(iii) Call by reference

(iv) Call by value

 

5. The appropriate solution of an equation f(x) =0 is:-

(i) x_n+1 = x_n f (nx)/f (xn)

(ii) x₂= x₁ f (nx)/f (xn)

(iii) x₁ = x₀ f (n)/f (n₀)

(iv) None of these.

 

6. Newtons backward difference interpolation formula is useful for interpolation near the end of:-

(i) Tabular values

(ii) Direct values

(iii) Indirect values

(iv) Both (b) and (c).

 

7. Equation

(i) Eular formula

(ii) Gauss forward formula

(iii) Lagrange polynomial of degree one passing through two points (x₀, y₀) and (x₁, y₁)

(iv) Stirrings interpolation divided difference formula.

 

 

8. Euler method uses:-

(i) Simples extrapolation techniques

(ii) Interpolation techniques.

(iii) Both (i) and (ii)

(iv) None of these.

 

 

9. A method which reduces the solution of the equation to an equivalent upper-triangular system and which can be solved by back substitution is called:

(i) N-R method

(ii) Gauss elimination method

(iii) Gauss-Jordan method

(iv) Matrix inversion.

 

10. Which is software:-

(i) CPU

(ii) Floppy

(iii) C++

(iv) Mouse.

 

 

 

Section:-B

 

Answer all five questions. Each carry 2 mark each.

 

Q.2 What are the various data types available in C? Explain them in brief.

Or

Write a program in C to point the sum of two numbers.

 

 

Q.3 Use the Newton-Raphson method to find the root of the equation x3-2x -5 =0

Or

Write an algorithm of Bisection-method to find the root of transcended equation.

 

 

Q.4 What do you mean by Eigen value and Eigen vector of matrices? Explain them in brief by giving suitable examples.

Or

Discuss what do you mean by numerical integration? Give suitable example.

 

 

Q.5 Explain Gauss backward formula to find differences which lie on the line.

 

Or

 

 

 

Find the missing term

X Y

0                                                  1

1                                                  3

2                                                  9

3                                                 

4                                                  81

Also explain why the result differs from 3³=27?

 

 

Q.7 Discuss in brief the Eulars method giving a suitable example.

Or

Use the Runge-Kutta fourth-order method to find the value of y, when x=1, given that y=1 when x=0 and that:

dy/dx=y-x/y+x

 

Section:-C

 

Answer any two of the following questions with detail. Each carry 10 mark each.

 

Q.7 What is the Output of the following printf () functions:-

(i) Printf (India\\Nepal\\Myanmar);

(ii) Printf (India\\\Nepal\\\Myanmar);

(iii) Printf (India\\\\Nepal\\\\Myanmar);

 

Q.8 (a) Use Gauss elimination method o solve:-

2x + y + z =10

3x +2y +3z =18

x + 4y +9z =16

(b) What is Pivoting? Why it is used in triangularization?

 

Q.9 What do you mean by Spline Fitting? Discuss it. Write its applications.

 

Q.10 Explain what are finite differences? Also discuss briefly Newtons for word and back word differences giving suitable example. Also obtain the sum:

S_n = 1³ +2³ +3³ ++ n³

 

Q.11 Write down general second-order linear partial differential equation. What problems arise when we study partial differential equation? Discuss them giving suitable illustrations.