AOE/ESM 2074 – Introduction to Computational
Methods
Final Exam
13 December 2000
This is a closed-book examination. Please turn in all your work and this
question sheet.
1. (15) Given a = rand(5,5) and b=[1: 5] decide which of
the following are well-defined. For those cases that are well-defined,
what is size(c) ?
i) c=b∗a
ii) c=a\b
iii) c=1./a
2. (15) Provide the necessary Matlab code(s) to approximatley locate the
minimum of the function f(x)=−xcos(x)ontheinterval[0,π/2].
3. (15) Apply one step of the bisection method to the problem of finding
a zero of
f(x)=x∗sin(x)−cos(x)
on the interval [0,π/2]. Note that f(0) = −1andthatf(π/2) = π/2.
You do not have to write any Matlab code for this problem.
4. (15) The Maclaurin expansion of exp(z)is
exp(z)=1+z+z2
2! +z3
3! +...
Writ e a M a t l a b s c r i p t .m file that will ask the user for a value of z
(possibly complex), ask the reader for a (positive) tolerance and sum
the series until the next term (the first term not included in the sum)
is smaller (in modulus) than the prescribed tolerance.
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