Solutions Manual for Introduction to Engineering and Scientific Computing with Python, 1st Edition by David Clough, Steven Chapra Chapters 1-10

Solutions Manual for Introduction to
Engineering and Scientific Computing with
Python, 1e by David Clough, Steven Chapra
(All Chapters)
Chapter 1
1.1 Express the following numbers in normalized scientific notation.

(a) 0.0001005 (b) 3.14159 (c) 62459100 (d) 602.2×1021

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(a) 1.005×10-4

(b) 3.14159×100

(c) 6.24591×107

(d) 6.022×1023


1.2 Carry out the following computations using a calculator or spreadsheet. Express the results
to the appropriate number of significant figures.
______
(a) 6.001 (b) 0.154)6.001 (c) 1.25×10-2 (d) 1.017×105  3.64×107
× 0.15_ 7.61×10-1
+ 3.06×10-3

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(a) 0.90015  0.90

(b) 38.9675...  39.0

(c) 0.77656  0.777


1.3 Round the following to the place indicated.

(a) 1047560 (b) 1.047 (c) 7450 (d) −15.43
to 1000 to 0.1 to 100 to 1




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(a) 1048000

(b) 1.0

(c) 7400

(d) -15
1.4 Rework problem 1.2b using long division.

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_38.9675...
0.154 ) 6.001
-4.620
0.1490
-0.1386
0.01040
-0.00924
0.001160
-0.001078
0.000082
-0.000077
0.000005
and so on


1.5 For the components and sum shown below, calculate the percentage each component is of
the total. Express your percentages with appropriate significant figures and ensure they sum
to 100%.
375
44
145
14
201
779

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375 0.481386 48%
44 0.056483 6%
145  0.186136  18%
14 0.017972 2%
201 0.258023 26%
779 1.0 100%

0.186... is rounded down because it has the least impact, about 0.1 above 0.5




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,1.6 Compute the following functions using a calculator or spreadsheet.

 
(a) sin (1.84 )
(b) tan  −  (c) cos ( 47.9 ) (d) tan −1 ( 25)
 4
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(a) -0.4817...

(b) -1

(c) cos(47.9*/180) = 0.6704...

(d) 1.5308...


1.7 Determine the roots of the following quadratic equations.

(a) x 2 + 0.20  x + 0.70 = 0 (b) x 2 − 28.4  x + 201.64 = 0

(c) 24  x 2 − 13  x = 0 (d) x 2 + 187  x − 24.0 = 0

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(a) -0.1  j 0.8307...

(b) 14.2, 14.2 (two equal roots)

(c) 0, 13/24  0.5417

(d) -187.13, 0.1282...




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, 1.8 Write down an approximate equation for the waveform shown in Figure P1.8.




Figure P1.8

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T = 15 − 3.5 = 11.5
2
=  0.546 rad/s
T
A = 1.5
 1 
1.5  sin (  0 +  ) = 1   = sin −1    0.730
 1.5 
y = 1.5  sin ( 0.546 t + 0.730 )


1.9 In the U.S., vehicle fuel economy is typically reported in miles per gallon (mpg). In Europe,
the common measure is liters per 100 km (L/100km). Americans would know a decent fuel
economy to be 40mpg. Help Europeans understand this by converting it to L/100km).

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mi 1.609 km gal km 1 L 100 L L
40    17.0    5.88
gal mi 3.785 L L 17.0 km 17.0 100 km 100 km




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