Author : Shigeru Kanemitsu
Publisher : World Scientific
ISBN 13 : 9811224501
Total Pages : 328 pages
Book Rating : 4.08/5 ( download)
Book Synopsis Analysis And Beyond: An Introduction With Examples And Exercises by : Shigeru Kanemitsu
Download or read book Analysis And Beyond: An Introduction With Examples And Exercises written by Shigeru Kanemitsu and published by World Scientific. This book was released on 2021-01-13 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its inverse — the change of variable — as well as the Leibniz rule and its inverse — the integration by parts. The chain rule or differentiation of composite functions is ubiquitous since almost all (a.a.) functions are composite functions of (elementary) functions and with the change of variable method as its reverse process. The Leibniz rule or differentiation of the product of two functions is essential since it makes differentiation nonlinear and with the method of integration by parts as its reverse process.Readers will find numerous worked-out examples and exercises in this volume. Detailed solutions are provided for most of the common exercises so that readers remain enthusiastically motivated in solving and understanding the concepts better.The intention of this volume is to lead the reader into the rich fields of advanced analysis and to obtain a much better view of useful mathematics.