Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 1, Problem 19P
You are working as a crime-scene investigator and must predict the temperature of a homicide victim over a 5-hr period. You know that the room where the victim was found was at 10°C when the body was discovered.
(a) Use Newton's law of cooling (Prob. 1.14) and Euler's method to compute the victim's body temperature for the 5-hr period using values of
(b) Further investigation reveals that the room temperature had actually dropped linearly from 20 to
(c) Compare the results from(a) and (b) by plotting them on the same graph.
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A surveyor sees a building across the river. Standing at point A he measures the angle of elevation
from the ground to the top of the building to be 30 degrees. He steps back 100 feet and again
measures the angle of elevation and finds it to be 15. (See Figure 12.26.) Assuming that it makes a
90-degree angle with the floor, approximately how tall is the building?
15
30°
100
A
river
Figure 12.26
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Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
AR and MA orders of this representation.
(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Chapter 1 Solutions
Numerical Methods for Engineers
Ch. 1 - Use calculus to solve Eq. (1.9) for the case where...Ch. 1 - 1.2 Repeat Example 1.2. Compute the velocity to ...Ch. 1 - Rather than the linear relationship of Eq. (1.7),...Ch. 1 - For the free-falling parachutist with linear drag,...Ch. 1 - Compute the velocity of a free-falling parachutist...Ch. 1 - 1.6 The following information is available for a...Ch. 1 - The amount of a uniformly distributed radioactive...Ch. 1 - A group of 35 students attend a class in a room...Ch. 1 - A storage tank contains a liquid at depth y, where...Ch. 1 - For the same storage tank described in Prob. 1.9,...
Ch. 1 - 1.11 Apply the conservation of volume (see Prob....Ch. 1 - In our example of the free-falling parachutist,...Ch. 1 - 1.13 Suppose that a spherical droplet of liquid...Ch. 1 - Newtons law of cooling says that the temperature...Ch. 1 - As depicted in Fig. P1.15, an RLC circuit consists...Ch. 1 - 1.16 Cancer cells grow exponentially with a...Ch. 1 - 1.17 A fluid is pumped into the network shown in...Ch. 1 - The velocity is equal to the rate of change of...Ch. 1 - You are working as a crime-scene investigator and...Ch. 1 - 1.21 As noted in Prob. 1.3, drag is more...Ch. 1 - 1.22 As depicted in Fig. P1.22, a spherical...Ch. 1 - As described in Prob. 1.22, in addition to the...Ch. 1 - As depicted in Fig. P1.24, the downward deflection...Ch. 1 - 1.25 Use Archimedes’ principle to develop a...Ch. 1 - Beyond fluids, Archimedes principle has proven...
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