Korovkin-Inequalities-LML torrent

Little Mathematics Library series
Inequalities by P. P. Korovkin

In this booklet the author did not pursue the aim of presenting the
basic properties of inequalities and made an attempt only to
familiarize students of senior classes with some particularly
remarkable inequalities playing an important role in various
sections of higher mathematics and with their use for finding the
greatest and the least values of quantities and for calculating some
limits. The book contains 63 problems, 35 of which are provided
with detailed solutions, composing thus its main subject, and 28
others are given in Sections 1.1 and 2.1, 2.3, 2.4 as exercises for
individual training. At the end of the book the reader will find
the solutions to the given exercises.


The book was translated the Russian by Sergei Vrubel and was
first published by Mir in 1975.

PDF | Cover | Bookmarks | OCR | 3.2 MB | 74 pp | 600 dpi

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Contents

Preface 6
Chapter 1. Inequalities 7
1.1. The Whole Part of a Number 7
1.2. The Arithmetic Mean and the Geometric Mean 12
1.3. The Number 19
1.4. The Bernoulli Inequality 23
1.5. The Mean Power of Numbers 27
Chapter 2. Uses of Inequalities 32
2.1. The Greatest and the Least Function Values 32
2.2. The Holder Inequality 40
2.3. The Use of Inequalities for Calculation of Limits 43
2.4. The Use of Inequalities for Approximate Calculation of Quantities 49
Solutions to Exercises 58