The Copperbelt University
School of Mathematics and Natural Sciences
Department of Mathematics
MA 411 : (Numerical Analysis and Statistics ) : Test two
June, 2024
Instructions Time Allowed : 2:00hrs
(1). You must write your Name, Student Identification Number (S.IN) and
Programme of study on your answer sheet.
(2). Calculators are allowed . Cell phones are Not allowed in this paper.
(3). There are two (2) questions in this paper, attempt all the questions and
show detailed working for full credit.
QUESTION ONE
be
(a) A fourier analysis of the instantaneous vcalue of a waveform can
represented by
)
=(t+)+sin t + sin3t.
near to 0.04.
Use Newton's Raphson method to determine the value of t
0.880.
correct to 4dp, when the amplitude y is
(5 marks)
(b) Given that
dy y
y(0) = 1,
dæ
steps)
find approximately y for z =0.1 by Euler's Modified method(5
(5 marks)
1
(c) Given that
dy 1
da
Taylor's method of
Dy considering the terms upto third degreeUse the
approximation to find the value of u when . t2 (5 marks)
0.4 taking n =0.1, if
(a) Use Runge - Kutta method And l at r= 0.2 and z =
dy
dæ
v(0) = 1.
(5 marks)
(e) Find the root of the eguation ze cOsz correct to four decimal places using
Regula -Falsi method.
(5 marks)
| Total = 25 marks 1
QUESTION TWO
(a) Use the Fixed point iteration method to find the root of the equation
sin z? cOs 4z =0,
that lies betwween 0.3 and 0.4.
(5 marks)
(b) Use an appropriate method to estimate, the value of 28 upto 4 decimal places.
(5 marks)
(c) Using Runge's method, obtain the solution of the equation
dy v(0) = 1
da
at the points = 0.1 and z = 0.2 and h=0.1
(5 marks)
(d) Obtain Picard's third approximate solution of the initial value problem upto
three (3) decimal place.
dy v(0) =0
da
(5 marks)
equation
(e) Determine the root of the
(z +3)3 el.92 + 5cos =9,
correct to 3 significant figures, using Bisection method.
(5 marks)
[ Total = 25 marks ]
END OF TEST
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