In this post, we will see the book Successive Approximation ( Popular Lectures In Mathematics 15) by N. Ya. Vilenkin.

About the book

The primary aim of this booklet is to present a number of methods for the approximate solution of equations. Their practical value is indisputable, yet they are little studied in high school or college. It will often happen, therefore, that someone who may even have majored in mathematics will find it difficult to solve the simplest of transcendental equations. Not only engineers but other specialists need to solve equations, and familiarity with methods of the approximate solution of equations is useful for the high school and college student.

Since most of the methods for the approximate solution of equations are connected with the concept of the derivative, we have found it necessary to introduce this concept. We have based our treatment on an appeal to geometry, however. The reader, therefore, needs no more background than is provided by high school mathematics.

In compiling this book, the author made use of a lecture he gave to ninth- and tenth-grade students in the school mathematics circle at Moscow State University. The content of this lecture was adopted by S. I. Shvartsburd, a Moscow high school teacher, for work outside class hours with his ninth-grade pupils. The author thanks him for his solutions to some of the problems used for this book.

The author expresses his deep gratitude to V. G. Boltyanskii, whose suggestions improved the first version of the manuscript.

Translated and Adapted from the Russian by Michael B.P. Slater and Joan W. Teller
Survey Of Recent East European Mathematical Literature
A Project Conducted By Alfred L. Putnam and Izaak Wirszup

Credits to original uploader.

You can get the book here.
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