03108nam 2200649 450 991080769690332120230807193417.03-11-035983-93-11-039916-410.1515/9783110359831(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, InfiniteMathematicsPhilosophyHistorySeries, Infinite.MathematicsPhilosophyHistory.515/.243SG 500-SG 600SEPArvkKörle Hans-Heinrich1934-1655376MiAaPQMiAaPQMiAaPQBOOK9910807696903321Infinite series in a history of analysis4007765UNINA