CSC204/214: COMPUTATIONAL SCIENCE AND NUMERICAL METHODS-FUO-EXAMS PAST QUESTIONS(FUOEXAMS)
CSC 204/214: COMPUTATIONAL SCIENCE AND NUMERICAL METHODS (Federal University Otuoke 1ST SEMESTER EXAMINATION 2017/2018 session)
Instruction:
answer 4 questions; all in section A and any 2 in section B.
SECTION A
1.
QUESTION ONE
a. With
illustration explain the following statements in relation to sources of error
in numerical analysis:
i.
An imperfect mathematical model of a physical system
ii.
Propagation of errors in floating point computations
iii.
Errors in measurements of parameters entering the
model
b. The width
of a rectangular piece of land is measured to be 48.25ft. If the measurement has a relative error εr of at most
2%, then what is an upper bound for the absolute error? Evolve codes in C++ or
Java that can be used to solve this problem.
2.
QUESTION TWO
a. Given that X0 = 1 is the initial
approximate root of Y = F(X) = X3
– 2X2 + 3, use the Newton’s method to evaluate X1, X2 and X3
b. Use the
iteration method to evaluate the approximate roots of the following: perform 3
iterations.
i.
165
ii.
160
iii.
130
Hence
sketch a skeletal program to perform this computation using C++ or Java.
SECTION B
3.
QUESTION THREE
a. Isaac
Newton devised a clever method to easily approximate the square root of a
number without having to use a calculator that has the square root function.
Describe this method with illustration.
b. Given that X0 = 2 is the initial
approximate root of Y = f(X) = 3X2 – 5X + 1, use the Newton’s method to evaluate X1 X2 and X3. Evolve codes in C++
or Java that can solve similar occurrences of this problem.
4.
QUESTION FOUR
a. The length of
a rectangular piece of land is measured to be 165ft ± 4inches. What are the relative
errors in this measured value?
b. Approximate
the roots of the following using the Newton’s method. Sketch a skeletal program
that performs this task; the program should terminate when the difference
between Xn and Xn-1 is less than 0.0001.
i.
29
ii.
68
iii.
72
5.
QUESTION FIVE
a. What
problems can be created by the following types of error
i.
Round off errors
ii.
Truncation errors
iii.
Programming errors
b. The
equation f(x) is given as X3
– X2 + 4X – 4 = 0. Considering the initial approximation at X =
2, then the values of the next 3 approximations correct up to 3
decimal places are:?
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