Mathematical analysis : functions, limits, series, continued fractions

✍ Scribed by Brown, Donald Edward; Lyusternik, Lazar' Aronovich; Spence, E.; Yanpol'skii, Avraam Ruvimovich

• Publisher: Pergamon Press
• Year: 1965
• Tongue: English
• Leaves: 407
• Series: International series of monographs in pure and applied mathematics Volume 69
• Edition: First edition
• Category: Library

✦ Synopsis

Mathematical Analysis: Functions, Limits, Series, Continued Fractions provides an introduction to the differential and integral calculus. This book presents the general problems of the theory of continuous functions of one and several variables, as well as the theory of limiting values for sequences of numbers and vectors.

Organized into six chapters, this book begins with an overview of real numbers, the arithmetic linear continuum, limiting values, and functions of one variable. This text then presents the theory of series and practical methods of summation. Other chapters consider the theory of numerical series and series of functions and other analogous processes, particularly infinite continued fractions. This book discusses as well the general problems of the reduction of functions to orthogonal series. The final chapter deals with constants and the most important systems of numbers, including Bernoulli and Euler numbers.

This book is a valuable resource for mathematicians, engineers, and research workers.

✦ Table of Contents

Content:
Front Matter,Copyright,FOREWORDEntitled to full textCHAPTER I - THE ARITHMETICAL LINEAR CONTINUUM AND FUNCTIONS DEFINED THERE, Pages 1-37
CHAPTER II - n-DIMENSIONAL SPACES AND FUNCTIONS DEFINED THERE, Pages 38-84
CHAPTER III - SERIES, Pages 85-169
CHAPTER IV - ORTHOGONAL SERIES AND ORTHOGONAL SYSTEMS, Pages 170-240
CHAPTER V - CONTINUED FRACTIONS, Pages 241-303
CHAPTER VI - SOME SPECIAL CONSTANTS AND FUNCTIONS, Pages 304-385
NOMENCLATURE, Pages 386-389
REFERENCES, Pages 390-395
INDEX, Pages 397-402
OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS, Pages 403-404