LEADER 03062oam 2200613I 450 001 9910800187403321 005 20230807204236.0 010 $a0-429-17240-0 010 $a1-4987-0266-X 024 7 $a10.1201/b17706 035 $a(CKB)2670000000567682 035 $a(EBL)1719856 035 $a(SSID)ssj0001367397 035 $a(PQKBManifestationID)11770870 035 $a(PQKBTitleCode)TC0001367397 035 $a(PQKBWorkID)11445112 035 $a(PQKB)10902747 035 $a(MiAaPQ)EBC1719856 035 $a(OCoLC)894169680 035 $a(EXLCZ)992670000000567682 100 $a20180331h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis with ultrasmall numbers /$fKarel Hrbacek, The City College of New York, USA, Olivier Lessmann, College Rousseau, Geneva, Switzerland, Richard O'Donovan, CEC Andre-Chavanne, Geneva, Switzerland 210 1$aBoca Raton :$cTaylor & Francis,$d[2015] 210 4$dİ2015 215 $a1 online resource (320 p.) 225 1 $aTextbooks in mathematics 300 $aA CRC title. 300 $aA Chapman and Hall book. 311 $a1-322-63387-8 311 $a1-4987-0265-1 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Contents; Preface; Preface for Students; Acknowledgments; Authors; Part I: Elementary Analysis; Chapter 1: Basic Concepts; Chapter 2: Continuity and Limits; Chapter 3: Differentiability; Chapter 4: Integration of Continuous Functions; Part II: Higher Analysis; Chapter 5: Basic Concepts Revisited; Chapter 6: L'Ho?pital's Rule and Higher Order Derivatives; Chapter 7: Sequences and Series; Chapter 8: First Order Differential Equations; Chapter 9: Integration; Chapter 10: Topology of Real Numbers; Answers to Exercises; Appendix: Foundations and Relative Set Theory; Bibliography 327 $aBack Cover 330 $aAnalysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon-delta methods. Students can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book is suitable for a calculus course at the undergraduate or high school level or for self-study with an emphasis on nonstandard 410 0$aTextbooks in mathematics (Boca Raton, Fla.) 606 $aCalculus 606 $aCalculus$xHistory 615 0$aCalculus. 615 0$aCalculus$xHistory. 676 $a515 700 $aHrbacek$b Karel$f1944,$01587200 702 $aLessmann$b Olivier 702 $aO'Donovan$b Richard$g(Richard John),$f1953- 801 0$bFlBoTFG 801 1$bFlBoTFG 906 $aBOOK 912 $a9910800187403321 996 $aAnalysis with ultrasmall numbers$93874663 997 $aUNINA