Analysis and beyond (Record no. 72771)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03227nam a2200373 a 4500 |
| 001 - CONTROL NUMBER | |
| control field | 00011943 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 210124s2021 si ob 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9789811224492 |
| -- | (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| -- | (hbk.) |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 515 |
| 100 1# - AUTHOR NAME | |
| Author | Kanemitsu, Shigeru |
| 245 10 - TITLE STATEMENT | |
| Title | Analysis and beyond |
| Sub Title | an introduction with examples and exercises / |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Singapore : |
| Publisher | World Scientific, |
| Year of publication | 2021. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (xiii, 313 p.) |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Preface -- Preliminaries -- Continuity of real numbers -- Limits and continuity -- Properties of continuous mappings -- Differentiation -- Properties of differentiable functions -- Extremal values, mean value theorems and taylor expansions in one variable -- Extremal values, mean value theorems and Taylor expansion in several variables -- Algorithms -- Theory of Riemann-Stieltjes integration -- Theory of Riemann integration -- Limit values and summability -- ODE and FDE -- Vector analysis -- Theory of distributions -- Topological spaces -- Appendices. Basics from linear algebra. Diagonalization of matrices. Circulants. Formulas for vector operations. Alternating algebras -- Bibliography -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | "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"--Publisher's website. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Kuzumaki, Takako, |
| 700 1# - AUTHOR 2 | |
| Author 2 | Liu, Jianya |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://www.worldscientific.com/worldscibooks/10.1142/11943#t=toc |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Calculus. |
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