| Level: Bachelor | Semester – Fall | Year: 2017 |
| Program: BCIS | Full Marks: 100 | |
| Course: Numerical Methods
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Pass Marks: 45 | |
| Time: 3hrs. | ||
| Candidates are required to give their answers in their own words as far as practicable. |
| The figures in the margin indicate full marks. |
| Section “A”
Very Short Answer Questions Attempt all the questions. |
10×2 |
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| 1. | Define Numerical error with its type. | ||||||||||||||||||||||||||||
| 2. | What is the necessary condition for the solution of a system of linear equations and what are the possible solutions? | ||||||||||||||||||||||||||||
| 3. | Define partial differential equations with examples. | ||||||||||||||||||||||||||||
| 4. | Why Gauss-Seidel method is better than Jacobi’s method? | ||||||||||||||||||||||||||||
| 5. | Differentiate between the bracketing and non-bracketing method of finding the solution of the nonlinear equations with examples. | ||||||||||||||||||||||||||||
| 6. | Define Interpolation and Regression. | ||||||||||||||||||||||||||||
| 7. | Solve the system of linear equations using the Matrix inverse method.
2x+3y=7 3x-y=5 |
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| 8. | Find f’(1) with h = 0.25 for f(x)=exp(x) – cos(x) using central difference formula. | ||||||||||||||||||||||||||||
| 9. | State the formula of Simpson’s 1/3rd rule? | ||||||||||||||||||||||||||||
| 10. | Find the normalized regression equation for the transcendental form
y = AeBx. |
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| Section “B”
Descriptive Answer Questions Attempt any six questions |
6×10 | ||||||||||||||||||||||||||||
| 11. | Using the False Position method, find the fourth root of 19 correct up to three decimal places. | ||||||||||||||||||||||||||||
| 12. | Differentiate between the Dollitle and Crout algorithm. Decompose the coefficient matrix into LU.
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| 13. | With an experiment of Thermal science, we observed the following data
If the relationship between the temperature (T) and time (t) is of the form T = Aet/4 + B. Estimate the temperature at t = 3.75min. |
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| 14. | Solve the differential equation by using classical RK method for y(0.5) from , y(0) = 1 with h=0.25 | ||||||||||||||||||||||||||||
| 15. | Integrate by using (n =4)
i) Trapezoidal rule ii) Simpson’s 1/3 rule |
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| 16. | Find the largest eigenvalue and the corresponding eigenvector of the Matrix using the power method.
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| 17. | In a square bar with a dimension of 3 inches ´ 3 inches, torsion function, Tian is obtained from the following P.D.E:
, where T = 0 on the outer boundary of the bar’s cross-section. Subdivide the region into nine equal squares to form a mesh and find the values of T in the interior nodes |
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| 18. | Section “C”
Case Analysis A body of mass 2 kg is attached to a spring with a spring constant of 10. The differential equation governing the displacement of the body y and time t is given by
Find the displacement y at time t = 0.2, given that y (0) = 0, y’(0) = 1. Use RK-2method.
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10
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| 19. | A company produces three different products. They are processed through three different departments D1, D2, and D3. The table below gives the number of hours that each department spends on each product.
Total Production hours available each month in each department is as follows:
a) Formulate the appropriate system of linear equations to determine the quantities of the three products that can be produced in each month, so that all the hours available in all departments are fully utilized. b) Determine how much time each department spends on each product. |
10 | |||||||||||||||||||||||||||
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