000			02682nam a22003257a 4500
003			OSt
005			20250508152438.0
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020			_a9783031916502
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a517.2 _bGHO-C
100	1		_aGhorpade, Sudhir R.
245	1	0	_aCourse in calculus and real analysis
250			_a2nd edition
260			_aCham, Switzerland : _bSpringer, _c2018.
300			_aix, 538 pages
490	0		_aUndergraduate texts in mathematics, _x0172-6056
504			_aIncludes bibliographical references and 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			_aCalculus
650			_aReal functions
650			_aSequences and series
650			_aDifferentiation
650			_aRiemann integrals
650			_aIntegration
700	1		_aLimaye, Balmohan V.
856			_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-01400-1/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/64528015-a-course-in-calculus-and-real-analysis?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cN
999			_c36035 _d36035