03101nam 2200649 450 991046143640332120200520144314.03-11-035983-93-11-039916-410.1515/9783110359831(CKB)3710000000482380(EBL)4006805(SSID)ssj0001557133(PQKBManifestationID)16180447(PQKBTitleCode)TC0001557133(PQKBWorkID)13980247(PQKB)11378301(MiAaPQ)EBC4006805(DE-B1597)426297(OCoLC)921347695(OCoLC)930487588(DE-B1597)9783110359831(Au-PeEL)EBL4006805(CaPaEBR)ebr11135107(CaONFJC)MIL838149(EXLCZ)99371000000048238020160121h20152015 uy 0engur|n|---|||||txtccrInfinite series in a history of analysis stages up to the verge of summability /Hans-Heinrich KörleBerlin, [Germany] ;Boston, [Massachusetts] :De Gruyter Oldenbourg,2015.©20151 online resource (142 p.)De Gruyter TextbookDescription based upon print version of record.3-11-034372-X Includes bibliographical references and index.Frontmatter -- Foreword -- Contents -- 1. The Greek era: Speculation, ideas and the comet of rigor -- 2. Successful experiments on infinite summation -- 3. Series of functions: the prototypes -- 4. Series seriously: the Greek comet reappears -- 5. On the verge of summability -- Appendixes (of notes, proofs, exercises) -- Life Data -- References -- Index"Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had helped it to a first high point when they mastered the infinite. The book traces the history of analysis along the risky route of serial procedures through antiquity. It took quite long for this type of mathematics to revive in our region. When and where it did, infinite series proved the driving force. Not until a good two millennia had gone by, would analysis head towards Greek rigor again. To follow all that trial, error and final accomplishment, is more than studying history: It provides touching, worthwhile access to advanced calculus. Moreover, some steps beyond convergence show infinite series to naturally fit a wider frame. De Gruyter textbook.Series, InfiniteMathematicsPhilosophyHistoryElectronic books.Series, Infinite.MathematicsPhilosophyHistory.515/.243Körle Hans-Heinrich1934-1034944MiAaPQMiAaPQMiAaPQBOOK9910461436403321Infinite series in a history of analysis2454369UNINA