test 1

UNIVERSITI TUN HUSSEIN ONN MALAYSIA

TEST 1

SEMESTER II

SESI 2013/2014

THIS QUESTION PAPER CONSISTS OF TWO (2) PAGES

COURSE NAME : ENGINEERING MATHEMATICS 4

COURSE CODE : BDA34003

PROGRAMME : BACHELOR OF MECHANICAL

ENGINEERING WITH HONOURS

EXAMINATION DATE : 1 APRIL 2014

DURATION : 1 HOURS 30 MINUTES

INSTRUCTION :

ANSWER ALL QUESTIONS

CONFIDENTIAL

CONFIDENTIAL

BDA34003

2

S1 Consider f(x) = x3 + 3x – 5.

Find a system at a stable condition (zero) in range [1,2]. Stop your prediction

when the error (convergence criteria) less than 0.001. Verify your calculation by

plotting the function, and show your predicted result is correct. By using:

(a) Secant method

(5 markah)

(b) Bisection Method

(5 markah)

S2 (a) Use Gaussian elimination with partial pivoting to solve the system of

linear equations given.

0.143x1 + 0.357x2 + 2.01x3 = - 5.173

−1.31x1 + 0.911x2 + 1.99x3 = - 5.458

11.2x1 − 4.30x2 − 0.605x3 = 4.415

(3 marks)

(b) Use the Crout reduction method to obtain an LU decomposition of the

matrix

(3 marks)

(c) Use the LU decomposition of (b) above to solve the linear system Mx=d

with M as in (b) and d= .

(4 marks)

S3 (a) The following data of the velocity of a body is given as a function of time.

Time (s) 10 15 18 22 24

Velocity (m/s) 22 24 37 25 123

A quadratic Lagrange interpolant is found using three data points, t=15, 18 and

22 (s). From this information, at what of the times given in seconds is the velocity

of the body, v=26(m/s) during the time interval of t=15 to t=22 seconds.

( 10 markah)