03502nam 22006255 450 991025406760332120200706210203.03-319-27807-X10.1007/978-3-319-27807-0(CKB)3710000000627477(SSID)ssj0001656926(PQKBManifestationID)16439717(PQKBTitleCode)TC0001656926(PQKBWorkID)14986639(PQKB)11106477(DE-He213)978-3-319-27807-0(MiAaPQ)EBC6311415(MiAaPQ)EBC5586418(Au-PeEL)EBL5586418(OCoLC)946011318(PPN)192774239(EXLCZ)99371000000062747720160330d2016 u| 0engurnn|008mamaatxtccrAdvanced Calculus of a Single Variable /by Tunc Geveci1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XII, 382 p. 88 illus., 77 illus. in color.) Bibliographic Level Mode of Issuance: Monograph3-319-27806-1 Preface -- Real Numbers, Sequences and Limits -- Limits and Continuity of Functions -- The Derivative -- The Riemann Integral -- Infinite Series -- Sequences and Series of Functions. Index. .This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.Integral transformsCalculus, OperationalFunctional analysisIntegral Transforms, Operational Calculushttps://scigraph.springernature.com/ontologies/product-market-codes/M12112Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Integral transforms.Calculus, Operational.Functional analysis.Integral Transforms, Operational Calculus.Functional Analysis.515Geveci Tuncauthttp://id.loc.gov/vocabulary/relators/aut755794MiAaPQMiAaPQMiAaPQBOOK9910254067603321Advanced calculus of a single variable1523063UNINA