LEADER 04553nam 22006015 450 001 9910300099003321 005 20250324063736.0 010 $a9783030014001 010 $a3030014002 024 7 $a10.1007/978-3-030-01400-1 035 $a(CKB)4100000007142700 035 $a(DE-He213)978-3-030-01400-1 035 $a(MiAaPQ)EBC6212355 035 $a(PPN)232470421 035 $a(EXLCZ)994100000007142700 100 $a20181116d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Course in Calculus and Real Analysis /$fby Sudhir R. Ghorpade, Balmohan V. Limaye 205 $a2nd ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (IX, 538 p.) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 311 08$a9783030013998 311 08$a3030013995 327 $a1. Numbers and Functions -- 2. Sequences -- 3. Continuity and Limits -- 4. Differentiation -- 5. Applications of Differentiation -- 6. Integration -- 7. Elementary Transcendental Functions -- 8. Applications and Approximations of Riemann Integrals -- 9. Infinite Series and Improper Integrals -- 10. Sequences and Series of Functions, Integrals Depending on a Parameter -- A. Construction of the Real Numbers -- B. Fundamental Theorem of Algebra -- References -- List of Symbols and Abbreviations -- Index. 330 $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. From reviews: [The first edition is] a rigorous, well-presented and original introduction to the core of undergraduate mathematics ? first-year calculus. It develops this subject carefully from a foundation of high-school algebra, with interesting improvements and insights rarely found in other books. [?] This book is a tour de force, and a necessary addition to thelibrary of anyone involved in teaching calculus, or studying it seriously. N.J. Wildberger, Aust. Math. Soc. Gaz. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aMathematical analysis 606 $aFunctions of real variables 606 $aSequences (Mathematics) 606 $aIntegral Transforms and Operational Calculus 606 $aReal Functions 606 $aSequences, Series, Summability 615 0$aMathematical analysis. 615 0$aFunctions of real variables. 615 0$aSequences (Mathematics) 615 14$aIntegral Transforms and Operational Calculus. 615 24$aReal Functions. 615 24$aSequences, Series, Summability. 676 $a515 700 $aGhorpade$b Sudhir R$4aut$4http://id.loc.gov/vocabulary/relators/aut$0501545 702 $aLimaye$b Balmohan V$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300099003321 996 $aA Course in Calculus and Real Analysis$92283971 997 $aUNINA