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Unformatted text preview: ASE 311 Engineering computation, Fall 2009, Homework 3
Due: Friday, September 18, 2:00 PM in the lecture room JGB 2.216
Report all work, including any mﬁles you have written. You may also ﬁnd the command diary
useful in recording your MATLAB session. Please write clearly and be sure to label for which problem
each solution is.
Please, staple Part I and Part II separately and make sure that your name is written on both parts.
Part I
1. [Chapra, Problem 6.1] Employ ﬁxedpoint iteration within MATLAB to locate the root of
√ () = 2 sin( ) − Use an initial guess of 0 = 0.5 and iterate until the approximate relative error is ≤ 0.01%.
2. [Divide and average method] Square root of 2 was computed using the formula
)
(
1
2
+1 = +
2 during one of the lectures. Derive this method from the NewtonRaphson formula.
Part II
3. [Mass of the bungee jumper] Let = 9.81 m/s2 and = 0.33 kg/m. Determine the mass for which the function
)
(√
√ () = tanh attains the value 40 m/s when = 5 s. Use MATLAB and the NewtonRaphson method. Compare your result with the one obtained using the builtin function fzero.
4. Write the following set of equations in matrix form:
50 = 53 − 72 42 + 73 + 30 = 0
1 − 73 = 40 − 32 + 51
What is the transpose of the coeﬃcient matrix?
5. A number of matrices are deﬁned as
⎡
⎡
⎤
⎤
4 7
1 0 1
[] = ⎣1 2⎦ , [] = ⎣0 2 3⎦ ,
5 6
4 0 0
(a)
(b)
(c)
(d) ⎡ ⎤
3
[] = ⎣−1⎦
0 What are the dimensions of the matrices?
What are the values of the elements 21 , 23 and 21 ?
Which of the following operations are possible: [] + [], [][], [][]?
Perform the possible operations manually. ...
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This note was uploaded on 10/01/2009 for the course ASE 311 taught by Professor Kraczek during the Spring '08 term at University of Texas at Austin.
 Spring '08
 KRACZEK

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