LEADER 03108nam 2200649 450 001 9910807696903321 005 20230807193417.0 010 $a3-11-035983-9 010 $a3-11-039916-4 024 7 $a10.1515/9783110359831 035 $a(CKB)3710000000482380 035 $a(EBL)4006805 035 $a(SSID)ssj0001557133 035 $a(PQKBManifestationID)16180447 035 $a(PQKBTitleCode)TC0001557133 035 $a(PQKBWorkID)13980247 035 $a(PQKB)11378301 035 $a(MiAaPQ)EBC4006805 035 $a(DE-B1597)426297 035 $a(OCoLC)921347695 035 $a(OCoLC)930487588 035 $a(DE-B1597)9783110359831 035 $a(Au-PeEL)EBL4006805 035 $a(CaPaEBR)ebr11135107 035 $a(CaONFJC)MIL838149 035 $a(EXLCZ)993710000000482380 100 $a20160121h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInfinite series in a history of analysis $estages up to the verge of summability /$fHans-Heinrich Ko?rle 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter Oldenbourg,$d2015. 210 4$dİ2015 215 $a1 online resource (142 p.) 225 1 $aDe Gruyter Textbook 300 $aDescription based upon print version of record. 311 $a3-11-034372-X 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tForeword -- $tContents -- $t1. The Greek era: Speculation, ideas and the comet of rigor -- $t2. Successful experiments on infinite summation -- $t3. Series of functions: the prototypes -- $t4. Series seriously: the Greek comet reappears -- $t5. On the verge of summability -- $tAppendixes (of notes, proofs, exercises) -- $tLife Data -- $tReferences -- $tIndex 330 $a"Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had helped it to a first high point when they mastered the infinite. The book traces the history of analysis along the risky route of serial procedures through antiquity. It took quite long for this type of mathematics to revive in our region. When and where it did, infinite series proved the driving force. Not until a good two millennia had gone by, would analysis head towards Greek rigor again. To follow all that trial, error and final accomplishment, is more than studying history: It provides touching, worthwhile access to advanced calculus. Moreover, some steps beyond convergence show infinite series to naturally fit a wider frame. 410 0$aDe Gruyter textbook. 606 $aSeries, Infinite 606 $aMathematics$xPhilosophy$xHistory 615 0$aSeries, Infinite. 615 0$aMathematics$xPhilosophy$xHistory. 676 $a515/.243 686 $aSG 500-SG 600$qSEPA$2rvk 700 $aKo?rle$b Hans-Heinrich$f1934-$01655376 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807696903321 996 $aInfinite series in a history of analysis$94007765 997 $aUNINA