Paperback. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

Title: Analysis And Beyond: An Introduction With Examples And Exercises (Paperback)
Publisher: World Scientific Publishing Co Pte Ltd, Singapore
Publication Date: 2021
Language: English
ISBN 10: 9819814049
ISBN 13: 9789819814046
Binding: Paperback
Condition: new

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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.

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