ANALYSIS & BEYOND : AN INTRODUCTION WITH EXAMPLES & EXERCISES

Takako Kuzumaki & Jia Shigeru Kanemitsu

ISBN 10: 9819814049 / ISBN 13: 9789819814046

Published by World Scientific, 2021

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Seller Inventory # 9789819814046

Bibliographic Details

• Title: ANALYSIS & BEYOND : AN INTRODUCTION WITH EXAMPLES & EXERCISES
• Publisher: World Scientific
• Publication Date: 2021
• Language: English
• ISBN 10: 9819814049
• ISBN 13: 9789819814046
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 18D millimeters 229 millimeters width by 152 millimeters height by 18 millimeters depth
• Weight: 477 grams

About this title

Synopsis

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.