PTU Punjab Technical University B-Tech May 2019 Question Papers 6th Semester CIVIL Engineering (CE)

Total No. of Pages : 02

Total No. of Questions : 09

B.Tech.(CE) (2011 Onwards) (Sem.?6)

NUMERICAL METHODS IN CIVIL ENGINEERING

Subject Code : BTCE-604

M.Code : 71085

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1.

SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks

each.

2.

SECTION-B contains FIVE questions carrying FIVE marks each and students

have to attempt any FOUR questions.

3.

SECTION-C contains T HREE questions carrying T EN marks each and students

have to attempt any T WO questions.

SECTION-A

Q1. Answer the following :

a) Define least square interpolation.

b) Find an interval containing a root of the equation x ? cos(x) = 0.

c) Explain Implicit solutions.

d) Determine the Lagrange interpolating polynomial passing through the points (2, 4) and

(5, 3).

e) Explain Explicit solutions.

f) Explain briefly the Newmarks procedure.

g) What is the order of convergence when Newton Raphson's method is applied to the

equation x2 ? 6x + 9 = 0 to find its multiple root.

h) Use the forward-difference formula to approximate the derivative of f(x) = In x at

x0 = 1.8 using h = 0.01.

i) Write a short note on bisection method.

j) Define initial value problem with a suitable example.

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SECTION-B

Q2. Use the Runge-Kutta method of order 4 ton approximate the solution of the following

initial value problem

y' = y ? t2 + 1, 0 t 2, y(0) = 0.5.

Q3. Apply Gauss Jordan method to find the inverse of the matrix

2

3

6

7

Q4. The following data is given :

1.0

1.3

1.6

1.9

2.2

0.7651977

0.6200860

0.4554022

0.2818186

0.1103623

Use Lagrange interpolation to approximate f(1.5) with x0 = 1.6.

Q5. Find a real root, correct to three decimal places of the equation 2x ? 3 = cos(x) lying in the

3

interval

,

.

2 2

Q6. Use Newton's iterative method to find the root of the equation 3x ? cos(x) + 1=0 starting

with an initial guess 0.6.

SECTION-C

Q7. Determine the values of h that will ensure an approximation error of less than 0.00002

when approximating

sin

xdx and employing :

0

a) Composite trapezoidal rule.

b) Composite Simpson's rule.

Q8. The function f(x) = tan x ? 6 has a zero at arctan6 0.447431543. Let p0 = 0 and

p1 = 0.48. Use ten iterations of the secant method to approximate this root.

Q9. A certain stimulus administered to each of the 12 patients resulted in the following increase

in blood pressure :

5, 2, 8, ?1, 3, 0, ?2, 1, 5, 0, 4, 6.

Can it be concluded that the stimulus will, in general, be accompanied by an increase in

blood pressure.

NOTE : Disclosure of identity by writing mobile number or making passing request on any

page of Answer sheet will lead to UMC case against the Student.

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This post was last modified on 04 November 2019