000			02541nam a22003137a 4500
003			OSt
005			20250730095906.0
008			250730b |||||||| |||| 00| 0 eng d
020			_a9783030013998
020			_a9783031916502 (pbk.) _c€ 49.99
040			_bENG _cIISER-BPR _dIISER-BPR
041			_aENG
082			_a515 _bGHO _223rd
100			_aGhorpade, Sudhir R. _95505
222			_aMathematics
245			_aA course in calculus and real analysis
250			_a2nd ed.
260			_aCham; Switzweland : _bSpringer Nature, _cc2018.
300			_aix, 538 p. : _bill. ; _c23cm.
440			_aUndergraduate Texts in Mathematics
504			_aIncludes illustrations, appendices, bibliographic reference, list of symbols and abbreviations and subject index.
520			_aOffering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single‐variable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof. Each chapter contains numerous examples and a large selection of exercises, as well as a “Notes and Comments” section, which highlights distinctive features of the exposition and provides additional references to relevant literature. This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises. A new chapter discusses sequences and series of real‐valued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter. Two new appendices cover a construction of the real numbers using Cauchy sequences, and a self‐contained proof of the Fundamental Theorem of Algebra. In addition to the usual prerequisites for a first course in single‐variable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs. This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis. The authors’ A Course in Multivariable Calculus is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting.
650			_aMathematics
650			_aAnalysis
650			_aCalculus
650			_aReal analysis
700			_aLimaye, Balmohan V. _93451
942			_2ddc _cBK
999			_c4279 _d4279