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008			210124s2021 si ob 001 0 eng
040			_a WSPC _b eng _c WSPC
020			_a9789811224492 _q(ebook)
020			_z9789811224485 _q(hbk.)
050	0	4	_aQA300 _b.K354 2021
072		7	_aMAT _x012020 _2bisacsh
072		7	_aMAT _x041000 _2bisacsh
072		7	_aMAT _x034000 _2bisacsh
082	0	4	_a515 _223
100	1		_aKanemitsu, Shigeru _921199
245	1	0	_aAnalysis and beyond _h[electronic resource] : _ban introduction with examples and exercises / _cShigeru Kanemitsu, Takako Kuzumaki, Jianya Liu.
260			_aSingapore : _bWorld Scientific, _c2021.
300			_a1 online resource (xiii, 313 p.)
504			_aIncludes bibliographical references and index.
505	0		_aPreface -- 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			_a"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.
538			_aMode of access: World Wide Web.
538			_aSystem requirements: Adobe Acrobat Reader.
650		0	_aMathematical analysis. _911486
650		0	_aCalculus. _921200
655		0	_aElectronic books. _93294
700	1		_aKuzumaki, Takako, _d1960- _921201
700	1		_aLiu, Jianya _c(Mathematics professor) _921202
856	4	0	_uhttps://www.worldscientific.com/worldscibooks/10.1142/11943#t=toc _zAccess to full text is restricted to subscribers.
942			_cEBK
999			_c72771 _d72771