Analysis And Beyond: An Introduction With Examples And Exercises
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€55.99
A01=Jianya Liu
A01=Shigeru Kanemitsu
A01=Takako Kuzumaki
Author_Jianya Liu
Author_Shigeru Kanemitsu
Author_Takako Kuzumaki
Category=PBK
Category=PBKS
Category=PBMS
Chain Rule vs. Change of Variable
Differentiation vs. Integration
Distribution
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Leibniz Rule vs. Integration by Parts
Local-Global Principle
Stieltjes Integrals
Unifying Sums and Integrals
Vector Analysis
Product details
- ISBN 9789819814046
- Publication Date: 03 Mar 2021
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Paperback
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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.
