January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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The last two types of interval are known as semi-open or semi-closed intervals.
Example
Express the following sets in terms of intervals.
a. fxAℝ: 23 # x , 5g
b. fxAℝ:jxj, 3g
c. fxAℝ:jx 2 1j# 2g
Solution
a. ½23; 5Þ
b. jxj, 3.23 , x , 3.ð23; 3Þ
c. x 2 1
jj
# 2.22 # x 2 1 # 2.22 1 1 # x # 2 1 1.21 # x #
3.½21; 3.
Example
–2 –1 0 1 2
–2 –1 0 1 2
–2 –1 0 1 2
–2 –1 0 1 2
–2 –1 0 1 2
–2 –1 0 1 2
–2 –1 0 1 2
–2 –1 0 1 2
(1, 2)
(1, 2)
(1, 2)
(1, ∞)
(1, ∞)
(–∞, 2)
(–∞, 2)
(–∞, ∞)
2.11 Complex Numbers
In algebra, we discovered that many equations are not satisfied by any real numbers.
Examples are
x
2
522orx
2
2 2x 1 40 5 0
We must introduce the concept of complex numbers.
25Elementary
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