Roots of an equation

A simple way of finding the roots of an equation, other than by divine inspiration, symmetry or guesswork is afforded by the Newton method. We start at some point denoted x l along the x-axis, and calculate the tangent to the curve at... 

S02(g) in the extraction of copper, rock-salt structure A crystal structure the same as that of a mineral form of sodium chloride, roentgen equivalent man rem The unit for reporting dose equivalent. See also sievert. root (of an equation) The solutions of the equation f(x) = 0. See also Appendix IE. root mean square speed c The square root of the average value of the squares of the speeds of the molecules in a sample. 

Newton s method) Suppose you want to find the roots of an equation g(x) = 0. Then Newton s method says you should consider the map , +i =/(- )> where... 

Fig. 8.1-1 The Newton-Raphson algorithm finds the root of an equation through iteration, of which the first three steps are shownhere.

A better method consists of calculating g as a root of an equation in g, by proceeding as indicated in Chapter 11, Section 3.3. We define w(z) by the equality... 

This is a preliminary operation to the determination of the roots by a process, perhaps simpler than the above. From (5), page 354, we see that if a, / , y,. .. are the roots of an equation of the wth degree,... 

Despite the infinite number of roots of eq. (10.20), it is often possible to determine analytically whether or not a given steady state Xg is stable. The problem is equivalent to deciding whether all the roots of an equation of the form [cf eq. (10.20)]... 

To find the roots of an equation f x) = 0, we start with a known approximate solution and apply any of the following methods. 

We first discuss the graphical method to obtain a numerical approximation to the root or roots of an equation. This method is useful because you can see what you are doing and you can usually be sure that you do not obtain a different root than the one you want to find. The equation to be solved is written in the form... 

Elementary ones such as finding the root of an equation, integration of a function or solving a set of linear equations. 

Write a program to find the root of an equation using the method of Regula Falsi. ... 

If this is being applied to the problem of finding a root of an equation, one assumes that one has a value Xj that is close to the value for which /(x) = 0 and the first order term can be used to approximate the solution value as ... 

---