Test 1
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Transcript of Test 1
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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
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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)