Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

594 Chapter 18 Mathematics in Engineering

4

10

5

0

 5

 10

 15

 20

021 468

x

2 x  4 y  10

4 x  y  6

y

■Figure 18.5

The plot of Equations

(18.5a) and (18.5b).

x (10 2 x)/ 46  4 x

0 2.5 6

0.5 2.25 4

12 2

1.5 1.75 0

2 1.5  2

2.5 1.25  4

31  6

3.5 0.75  8

4 0.5  10

4.5 0.25  12

50  14

5.5 0.25  16

6 0.5  18

Systems of Linear Equations

At times, the formulation of an engineering problem leads to a set of linear equations that

must be solved simultaneously. In Section 18.5, we will discuss the general form for such

problems and the procedure for obtaining a solution. Here, we will discuss a simple graph-

ical method that you can use to obtain the solution for a model that has two equations

with two unknowns. For example, consider the following equations withxandyas unknown

variables.

(18.5a)

(18.5b)

Equations (18.5a) and (18.5b) are plotted and shown in Figure 18.5. The intersection of the

two lines represents thexsolution, which is given byx1; because as you can see atx1,

both equations have the sameyvalue. We then substitute forxinto either Equation (18.5a) or

Equation (18.5b) and solve fory, which yields a value ofy2.

18.3 Nonlinear Models

For many engineering situations, nonlinear models are used to describe the relationships

between dependent and independent variables because they predict the actual relationships

more accurately than linear models do. In this section, we first discuss some examples of engi-

neering situations where nonlinear mathematical models are found. We then explain some of

the basic characteristics of nonlinear models.

4 xy 6

2 x 4 y 10

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