Newton’s Method

Brian Knight and Roger Adams
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Brian Knight: Goldsmiths’ College
Roger Adams: Thames Polytechnic

Chapter 10 in Calculus I, 1975, pp 67-71 from Springer

Abstract: Abstract Many of the equations arising in practical problems are of a type difficult or impossible to solve by the standard algebraic methods. For example, the equations: 2 sin x − x = 0 e x − 2 x − 1 = 0 , x 6 − 3 x + 1 = 0 $$ 2\sin {\kern 1pt} x - x = 0{\kern 1pt} {\kern 1pt} {e^x} - 2x - 1 = 0,{\kern 1pt} {\kern 1pt} {x^6} - 3x + 1 = 0 $$ have roots which we may estimate, by graphing the functions and finding where the graphs cut the x-axis, but which we cannot find exactly. In these cases a numerical procedure known as Newton’s method allows us to use a value x 0 which is an approximate root of the equation: f ( x ) = 0 $$ f(x) = 0 $$ in order to obtain a better approximation x 1.

Date: 1975
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DOI: 10.1007/978-1-4615-6594-9_10

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