2009 | OriginalPaper | Buchkapitel
Roots of Nonlinear Equations
Verlag: Springer Netherlands
A large number of engineering and scientific problems can be formulated in terms of finding the value, or values, of some variable x which results in a zero value of some function of that variable. Mathematically, this is represented by the equation
(3.1)
$$F\left( x \right) = 0,$$
where
F
(x) is some given function of x. Examples are polynomial equations such as
(3.2)
$$F\left( x \right) = 5x^4 - 4x^2 + 2x - 3 = 0,$$
or transcendental equations such as
(3.3)
$$F\left( x \right) = \tan \left( x \right) - 1/x.$$
For the case of polynomial equations, the solution values of x which satisfy the equation are frequently called “Croots” of the polynomial. In general these may be real numbers or complex numbers. For the case of transcendental equations such as Eq. (
3.3
) the solution values are typically called “zeros” of the function. Mathematically the terms roots and zeros are used interchangeably.
