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SUMMER 2014, ASSIGNMENT
| DRIVE | SUMMER 2014 |
| PROGRAM | BACHELOR OF COMPUTER APPLICATION |
| SUBJECT CODE & NAME | BCA3010 -COMPUTER ORIENTED NUMERICAL METHODS |
| SEMESTER | THIRD |
| CREDITS | 4 |
| MAX. MARKS | 60 |
| BK ID | B |
Answer all questions
- 1 Solve the system of equation by matrix inversion method
x +y +z = 1
x +2y + 3z = 6
x + 3y +4z = 6
Solution:-Write the given as a single matrix equation:
- 1 1 x 1
1 2 3 y = 6
1 3 4 z 6
This is called matrix product.
- 2. Find all eigen values and the corresponding eigen vectors of the matrix.
A = I 8 – 6 2 I
I 6 7 4 I
I 2 4 3 I
- 3. Find the cubic polynomial which takes the following values y(0) = 1, y(1) = 0, y(2) = 1 and y(3) = 10. Hence or otherwise, obtain y (0.5).
Solution: –
y = ax^3 + bx^2 = cx +d.
y(0) = 1 = 0+0+0+d, d = 1
y(1) = 0 = a+b+c+1, a+b+c = -1
- 4. Find the approximate value of ò p/2,0 √ cos q dq by Simpson’s 1/3rd rule by dividing [0, p/2] into 6 equal parts.
Solution:- A method for approximating the value of a function near a known value. The method uses the tangent line at the known value of the function to approximate the function’s graph. In this method Δx and Δy represent the changes in x and y for the function, and dx and dy represent the changes in x and y for the tangent line.
- 5. Use Picard’s method of successive approximations to find y1,y2, y3 to the solution of the initial value problem
Solution:-
Y ‘ = y
Y(0) = 1
We know that it has a unique solution.
The integral equation equivalent to this
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