LEADER 01109nam0-2200349li-450 001 990000141040203316 005 20180312154801.0 035 $a0014104 035 $aUSA010014104 035 $a(ALEPH)000014104USA01 035 $a0014104 100 $a20001109d1989----km-y0itay0103----ba 101 0 $aita 102 $aIT 200 1 $aBugs and bugbears$edizionario delle insidie e dei tranelli nelle traduzioni fra inglese e italiano$fdi Virginia Browne e Gabriele Natali 210 $aBologna$cZanichelli$dcopyr. 1989 215 $a251 p.$c25 cm 610 1 $alingua inglese dizionari italiani 700 1$aBrowne,$bVirginia$0355457 702 1$aNATALI,$bGabriele 801 $aSistema bibliotecario di Ateneo dell' Universitā di Salerno$gRICA 912 $a990000141040203316 951 $aREF 421 BRO$b0000767 959 $aBK 969 $aTEC 979 $c19931018 979 $c20001110$lUSA01$h1712 979 $aPATRY$b90$c20010830$lUSA01$h1225 979 $c20020403$lUSA01$h1621 979 $aPATRY$b90$c20040406$lUSA01$h1610 996 $aBugs and bugbears$91501266 997 $aUNISA LEADER 06351nam 2200505 450 001 996466387403316 005 20230621200300.0 010 $a3-030-77139-3 035 $a(CKB)5340000000068547 035 $a(MiAaPQ)EBC6792502 035 $a(Au-PeEL)EBL6792502 035 $a(OCoLC)1280604499 035 $a(PPN)25829681X 035 $a(EXLCZ)995340000000068547 100 $a20220718d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSharpening mathematical analysis skills /$fAlina Sintamarian, Ovidiu Furdui 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (543 pages) 225 1 $aProblem Books in Mathematics,$x2197-8506 311 $a3-030-77138-5 327 $aIntro -- Preface -- Contents -- Notations -- Part I Theory and Problems -- 1 Sequences of Real Numbers -- 1.1 Limits of Sequences -- 1.2 Applications of Stolz-Cesāro Theorem, the ?/? and the 0/0 Cases -- 1.3 Wolstenholme Sequences -- 1.4 Limits of Integrals -- 2 Series of Real Numbers -- 2.1 Miscellaneous Series -- 2.2 Applications of Abel's Summation Formula -- 2.3 Series with Positive Terms -- 2.4 Alternating Series -- 2.5 Series with Harmonic Numbers and Factorials -- 2.6 A Mosaic of Series -- 3 Power Series -- 3.1 Convergence and Sum of Power Series -- 3.2 Maclaurin Series of Elementary Functions -- 3.3 Gems with Numerical and Power Series -- 3.4 Single Zeta Series -- 3.5 Polylogarithm Series -- 3.6 Inequalities and Integrals -- 3.7 Generating Functions -- 3.8 Series with Harmonic and Skew-Harmonic Numbers -- 3.9 Remarkable Numerical and Function Series -- 3.10 Multiple Series with the Riemann Zeta Function -- 3.11 Series Involving Products of Harmonic Numbers -- 4 Derivatives and Applications -- 4.1 Apéritif -- 4.2 Integral Equations -- 4.3 Differential Equations -- 4.4 Higher Order Derivatives -- 4.5 Taylor's Formula -- 4.6 Series with the Maclaurin Remainder of a Function f -- 4.7 Series with Fractional Part Function -- 4.8 Extrema of One Variable Functions -- 5 Partial Derivatives and Applications -- 5.1 Partial Derivatives, the Jacobian and the Hessian Matrices, Differential Operators -- 5.2 The Chain Rule -- 5.3 Homogeneous Functions. Euler's Identity -- 5.4 Taylor's Formula for Real Functions of Two Real Variables -- 5.5 The Differential of Several Real Variable Functions -- 5.6 Extrema of Several Real Variable Functions -- 6 Implicit Functions -- 6.1 Implicit Functions of One Real Variable Defined by an Equation -- 6.2 Implicit Functions of Two Real Variables Defined by an Equation. 327 $a6.3 Implicit Functions of One Real Variable Defined by a System of Equations -- 6.4 Implicit Functions of Two Real Variables Defined by a System of Equations -- 7 Challenges, Gems, and Mathematical Beauties -- 7.1 Limits of Sequences -- 7.2 Limits of Integrals -- 7.3 Convergence and Evaluation of Series -- 7.4 Harmonic Series -- 7.5 Series with Factorials -- 7.6 Series of Functions -- 7.7 Pearls of Series with Tails of Zeta Function Values -- 7.8 Exotic Zeta Series -- 7.9 Special Differential Equations -- 7.10 Inequalities -- 7.11 Fabulous Integrals -- 8 An Artistry of Quadratic Series: Two New Proofs of Sandham-Yeung Series -- 8.1 The First Proof -- 8.2 The Second Proof -- Part II Solutions -- 9 Sequences of Real Numbers -- 9.1 Limits of Sequences -- 9.2 Applications of Stolz-Cesāro Theorem, the ?/? and the 0/0 Cases -- 9.3 Wolstenholme Sequences -- 9.4 Limits of Integrals -- 10 Series of Real Numbers -- 10.1 Miscellaneous Series -- 10.2 Applications of Abel's Summation Formula -- 10.3 Series with Positive Terms -- 10.4 Alternating Series -- 10.5 Series with Harmonic Numbers and Factorials -- 10.6 A Mosaic of Series -- 11 Power Series -- 11.1 Convergence and Sum of Power Series -- 11.2 Maclaurin Series of Elementary Functions -- 11.3 Gems with Numerical and Power Series -- 11.4 Single Zeta Series -- 11.5 Polylogarithm Series -- 11.6 Inequalities and Integrals -- 11.7 Generating Functions -- 11.8 Series with Harmonic and Skew-Harmonic Numbers -- 11.9 Remarkable Numerical and Function Series -- 11.10 Multiple Series with the Riemann Zeta Function -- 11.11 Series Involving Products of Harmonic Numbers -- 12 Derivatives and Applications -- 12.1 Apéritif -- 12.2 Integral Equations -- 12.3 Differential Equations -- 12.4 Higher Order Derivatives -- 12.5 Taylor's Formula -- 12.6 Series with the Maclaurin Remainder of a Function f. 327 $a12.7 Series with Fractional Part Function -- 12.8 Extrema of One Variable Functions -- 13 Partial Derivatives and Applications -- 13.1 Partial Derivatives, the Jacobian and the Hessian Matrices, Differential Operators -- 13.2 The Chain Rule -- 13.3 Homogeneous Functions. Euler's Identity -- 13.4 Taylor's Formula for Real Functions of Two Real Variables -- 13.5 The Differential of Several Real Variable Functions -- 13.6 Extrema of Several Real Variable Functions -- 14 Implicit Functions -- 14.1 Implicit Functions of One Real Variable Defined by an Equation -- 14.2 Implicit Functions of Two Real Variables Defined by an Equation -- 14.3 Implicit Functions of One Real Variable Defined by a System of Equations -- 14.4 Implicit Functions of Two Real Variables Defined by a System of Equations -- 15 Challenges, Gems, and Mathematical Beauties -- 15.1 Limits of Sequences -- 15.2 Limits of Integrals -- 15.3 Convergence and Evaluation of Series -- 15.4 Harmonic Series -- 15.5 Series with Factorials -- 15.6 Series of Functions -- 15.7 Pearls of Series with Tails of Zeta Function Values -- 15.8 Exotic Zeta Series -- 15.9 Special Differential Equations -- 15.10 Inequalities -- 15.11 Fabulous Integrals -- References -- Index. 410 0$aProblem books in mathematics. 606 $aMathematical analysis 606 $aAnālisi matemātica$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematical analysis. 615 7$aAnālisi matemātica 676 $a515 700 $aSintamarian$b Alina$01072426 702 $aFurdui$b Ovidiu 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466387403316 996 $aSharpening mathematical analysis skills$92900985 997 $aUNISA