LEADER 06777nam 22005772 450 001 9910814891603321 005 20151002020706.0 010 $a1-61444-209-6 035 $a(CKB)2560000000081401 035 $a(SSID)ssj0000577625 035 $a(PQKBManifestationID)11347937 035 $a(PQKBTitleCode)TC0000577625 035 $a(PQKBWorkID)10576756 035 $a(PQKB)10272527 035 $a(UkCbUP)CR9781614442097 035 $a(MiAaPQ)EBC3330374 035 $a(Au-PeEL)EBL3330374 035 $a(CaPaEBR)ebr10728523 035 $a(OCoLC)929120469 035 $a(RPAM)14779275 035 $a(EXLCZ)992560000000081401 100 $a20120305d2007|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA garden of integrals /$fFrank Burk$b[electronic resource] 210 1$aWashington :$cMathematical Association of America,$d2007. 215 $a1 online resource (xiv, 281 pages) $cdigital, PDF file(s) 225 0 $aDolciani Mathematical Expositions, $vv. 31 225 0$aDolciani mathematical expositions ;$vno. 31 300 $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015). 311 $a0-88385-356-6 311 $a0-88385-337-X 320 $aIncludes bibliographical references and index. 327 $tForeword --$gAn historical overview --$g1.1.$tRearrangements --$g1.2.$tThe lune of Hippocrates --$g1.3.$tExdoxus and the method of exhaustion --$g1.4.$tArchimedes' method --$t1.5.$tGottfried Leibniz and Isaac Newton --$g1.6.$tAugustin-Louis Cauchy --$g1.7.$tBernhard Riemann --$g1.8.$tThomas Stieltjes --$g1.9.$tHenri Lebesgue --$g1.10.$tThe Lebesgue-Stieltjes integral --$g1.11.$tRalph Henstock and Jaroslav Kurzweil --$g1.12.$tNorbert Wiener --$g1.13.$tRichard Feynman --$g1.14.$tReferences --$g2.$tThe Cauchy integral --$g2.1.$tExploring integration --$g2.2.$tCauchy's integral --$g2.3.$tRecovering functions by integration --$g2.4.$tRecovering functions by differentiation --$g2.5.$tA convergence theorem --$g2.6.$tJoseph Fourier --$g2.7.$tP.G. Lejeune Dirichlet --$g2.8.$tPatrick Billingsley's example --$g2.9.$tSummary --$g2.10.$tReferences --$g3.$tThe Riemann integral --$g3.1.$tRiemann's integral --$g3.2.$tCriteria for Riemann integrability --$g3.3.$tCauchy and Darboux criteria for Riemann integrability --$g3.4.$tWeakening continuity --$g3.5.$tMonotonic functions are Riemann integrable --$g3.6.$tLebesgue's criteria --$g3.7.$tEvaluating a? la Riemann --$g3.8.$tSequences of Riemann integrable functions --$g3.9.$tThe Cantor set --$g3.10.$tA nowhere dense set of positive measure --$g3.11.$tCantor functions --$g3.12.$tVolterra's example --$g3.13.$tLengths of graphs and the Cantor function --$g3.14.$tSummary --$g3.15.$tReferences. 327 $g4.$tRiemann-Stieltjes integral --$g4.1.$tGeneralizing the Riemann integral--$g4.2.$tDiscontinuities --$g4.3.$tExistence of Riemann-Stieltjes integrals --$g4.4.$tMonotonicity of [null] --$g4.5.$tEuler's summation formula --$g4.6.$tUniform convergence and R-S integration --$g4.7.$tReferences --$g5.$tLebesgue measure --$g5.1.$tLebesgue's idea --$g5.2.$tMeasurable sets --$g5.3.$tLebesgue measurable sets and Carathe?odory --$g5.4.$tSigma algebras --$g5.5.$tBorel sets --$g5.6.$tApproximating measurable sets --$g5.7.$tMeasurable functions --$g5.8.$tMore measureable functions --$g5.9.$tWhat does monotonicity tell us? --$g5.10.$tLebesgue's differentiation theorem --$g5.11.$tReferences --$g6.$tThe Lebesgue-Stieltjes integral --$g6.1.$tIntroduction --$g6.2.$tIntegrability : Riemann ensures Lebesgue --$g6.3.$tConvergence theorems --$g6.4.$tFundamental theorems for the Lebesgue integral --$g6.5.$tSpaces --$g6.6.$tL²[-pi, pi] and Fourier series --$g6.7.$tLebesgue measure in the plane and Fubini's theorem --$g6.8.$tSummary--$tReferences --$g7.$tThe Lebesgue-Stieltjes integral --$g7.1.$tL-S measures and monotone increasing functions --$g7.2.$tCarathe?odory's measurability criterion --$g7.3.$tAvoiding complacency --$g7.4.$tL-S measures and nonnegative Lebesgue integrable functions --$g7.5.$tL-S measures and random variables --$g7.6.$tThe Lebesgue-Stieltjes integral --$g7.7.$tA fundamental theorem for L-S integrals --$g7.8.$tReferences. 327 $g8.$tThe Henstock-Kurzweil integral --$g8.1.$tThe generalized Riemann integral --$g8.2.$tGauges and [infinity]-fine partitions --$g8.3.$tH-K integrable functions --$g8.4.$tThe Cauchy criterion for H-K integrability --$g8.5.$tHenstock's lemma --$g8.6.$tConvergence theorems for the H-K integral --$g8.7.$tSome properties of the H-K integral --$g8.8.$tThe second fundamental theorem --$g8.9.$tSummary--$g8.10.$tReferences --$g9.$tThe Wiener integral --$g9.1.$tBrownian motion --$g9.2.$tConstruction of the Wiener measure --$g9.3.$tWiener's theorem --$g9.4.$tMeasurable functionals --$g9.5.$tThe Wiener integral --$g9.6.$tFunctionals dependent on a finite number of t values --$g9.7.$tKac's theorem --$g9.8.$tReferences --$g10.$tFeynman integral --$g10.1.$tIntroduction --$g10.2.$tSumming probability amplitudes --$g10.3.$tA simple example --$g10.4.$tThe Fourier transform --$g10.5.$tThe convolution product --$g10.6.$tThe Schwartz space --$g10.7.$tSolving Schro?dinger problem A --$g10.8.$tAn abstract Cauchy problem --$g10.9.$tSolving in the Schwartz space --$g10.10.$tSolving Schro?dinger problem B --$g10.11.$tReferences --$tIndex --$tAbout the author. 330 $aThe derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there are a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman. The basic properties of each are proved, their similarities and differences are pointed out, and the reason for their existence and their uses are given. Historical information is plentiful. Advanced undergraduate mathematics majors, graduate students, and faculty members are the audience for the book. Even experienced faculty members are unlikely to be aware of all of the integrals in the Garden of Integrals and the book provides an opportunity to see them and appreciate the richness of the idea of integral. Professor Burke's clear and well-motivated exposition makes this book a joy to read. 606 $aIntegrals 615 0$aIntegrals. 676 $a515/.43 700 $aBurk$b Frank$0253701 702 $aScully$b Terence$f1935- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910814891603321 996 $aA garden of integrals$93914865 997 $aUNINA LEADER 00987nam0 22002651i 450 001 UON00524226 005 20240422051655.126 100 $a20240422d1962 |0itac50 ba 101 $adut 102 $aNL 105 $a|||| ||||| 200 1 $aGramarie$ekeur uit het werk van zijn hoogteraarstijd$fC. B. van Haeringen 210 $aAssen$cvan Gorcum$d1962 215 $a381 p.$d25 cm. 606 $aLingua Neerdenlandese$3UONC048332$2FI 620 $aNL$dAssen$3UONL001352 676 $a439.31$cLingue neerlandesi. Olandese$v21 700 1$aHAERINGEN$bCoenraad Bernardus : van$3UONV165503$0713481 712 $aVan Gorcum$3UONV245911$4650 801 $aIT$bSOL$c20250509$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00524226 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI Oland Ling 132 $eSI FG 572/1 5 132 996 $aGramarie$94376167 997 $aUNIOR LEADER 03529nam 2200529 a 450 001 9911020273603321 005 20251116152201.0 010 $a3-527-61953-4 035 $a(CKB)1000000000376634 035 $a(MH)009711146-5 035 $a(SSID)ssj0000354454 035 $a(PQKBManifestationID)11264322 035 $a(PQKBTitleCode)TC0000354454 035 $a(PQKBWorkID)10302591 035 $a(PQKB)10890542 035 $a(MiAaPQ)EBC481815 035 $a(PPN)243246528 035 $a(EXLCZ)991000000000376634 100 $a20070724d2004 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMetal-catalyzed cross-coupling reactions /$fedited by Armin de Meijere and Franc?ois Diederich 205 $aSecond, completely revised and enlarged edition. 210 $aWeinheim $cWiley-VCH$dc2004 215 $a1 online resource (xxii, 2 v. )$cill. ; 300 $aDiederich's name appears first on the earlier edition. 311 08$a3-527-30518-1 320 $aIncludes bibliographical references and index. 327 $aMechanic aspects of metal-catalyzed C, C- and C, X-bond-forming reactions / Antonio M. Echavarren and Diego J. Cárdenas -- Metal-catalyzed cross-coupling reactions of organoboron compounds with organic halides / Norio Miyaura -- Organotin reagents in cross-coupling reactions / Terence N. Mitchell -- Organosilicon compounds in cross-coupling reactions / Scott E. Denmark and Ramzi F. Sweis -- Cross-coupling of organyl halides with alkenes: the Heck reaction / Stefan Bräse and Armin de Meijere -- Cross-coupling reactions to sp carbon atoms / Jeremiah A. Marsden and Michael M. Haley -- Carbometallation reactions / Ilan Marek, Nicka Chinkov, and Daniella Banon-Tenne -- Palladium-catalyzed 1,4-additions to conjugated dienes / Jan-E. Bäckvall -- Cross-coupling reactions via [pi]-allylmetal intermediates / Uli Kazmaier and Matthias Pohlman -- Palladium-catalyzed coupling reactions of propargyl compounds / Jiro Tsuji and Tadakatsu Mandai -- Carbon-carbon bond-forming reactions mediated by organozinc reagents / Paul Knochel, M. Isabel Calaza, and Eike Hupe -- Carbon-carbon bond-forming reactions mediated by organomagnesium reagents / Paul Knochel, Ioannis Sapountzis, and Nina Gommermann -- Palladium-catalyzed aromatic carbon-nitrogen bond formation / Lei Jiang and Stephen L. Buchwald -- The directed ortho-metallation (DoM) cross-coupling nexus, synthetic methodology for the formation of aryl-aryl and aryl-heteroatom-aryl bonds / Eric J.-G. Anctil and Victor Snieckus -- Palladium- or nickel-catalyzed cross-coupling with organometals containing zinc, aluminum, and zirconium: the Negishi coupling / Ei-ichi Negishi, Xingzhong Zeng, Ze Tan, Mingxing Qian, Qian Hu, and Zhihong Huang. 606 $aOrganic compounds$xSynthesis 606 $aMetal catalysts 615 0$aOrganic compounds$xSynthesis. 615 0$aMetal catalysts. 676 $a547/.2 700 $aMeijere$b A. de$0477714 701 $aDiederich$b Franc?ois$0543126 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020273603321 996 $aMetal-catalyzed cross-coupling reactions$94421410 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress