Civil Engineering Reference
In-Depth Information
cHAPtER 1
r
oots
of
A
LgebrAic
And
t
rAnscendentAL
e
quAtions
In structural engineering, it is important to have a basic knowledge of how
computers and calculators solve equations for unknowns. Some equations
are solved simply by algebra while higher order equations will require
other methods to solve for the unknowns. In this chapter, methods of find-
ing roots to various equations are explored. The
roots
of an equation are
defined as values of
x
where the solution of an equation is true. The most
common roots are where the value of the function is zero. This would
indicate where a function crosses an axis. Roots are sometimes
complex
roots
where they contain both a real number and an imaginary unit.
1.1 EQuAtiOnS
Equations are generally grouped into two main categories, algebraic equa-
tions and transcendental equations. The first type, an
algebraic equation
,
is defined as an equation that involves only powers of
x
. The powers of
x
can be any real number whether positive or negative. The following are
examples of algebraic equations:
83560
1
x
3
−+−=
x
2
x
+
2
x
=
0
x
125
.
x
−=
30
p
The second type is
transcendental equations
. These are non-algebraic
equations or functions that transcend, or cannot be expressed in terms of
