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[null,"1.","Record Nr.",null,"UNISA996466387403316"]
[null,null,"Autore",null,"Sintamarian Alina"]
[null,null,"Titolo",null,"Sharpening mathematical analysis skills / / Alina Sintamarian, Ovidiu Furdui"]
[null,null,"Pubbl/distr/stampa",null,"Cham, Switzerland : , : Springer, , [2021]"]
[{"$nulls":4},"©2021"]
[null,null,"ISBN",null,"3-030-77139-3"]
[null,null,"Descrizione fisica",null,"1 online resource (543 pages)"]
[null,null,"Collana",null,"Problem Books in Mathematics, , 2197-8506"]
[null,null,"Disciplina",null,"515"]
[null,null,"Soggetti",null,"Mathematical analysis"]
[{"$nulls":4},"Anàlisi matemàtica"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Intro -- Preface -- Contents -- Notations -- Part I Theory and Problems -- 1 Sequences of Real Numbers -- 1.1 Limits of Sequences -- 1.2 Applications of Stolz-Cesàro Theorem, the ∞/∞ and the 0/0 Cases -- 1.3 Wolstenholme Sequences -- 1.4 Limits of Integrals -- 2 Series of Real Numbers -- 2.1 Miscellaneous Series -- 2.2 Applications of Abel's Summation Formula -- 2.3 Series with Positive Terms -- 2.4 Alternating Series -- 2.5 Series with Harmonic Numbers and Factorials -- 2.6 A Mosaic of Series -- 3 Power Series -- 3.1 Convergence and Sum of Power Series -- 3.2 Maclaurin Series of Elementary Functions -- 3.3 Gems with Numerical and Power Series -- 3.4 Single Zeta Series -- 3.5 Polylogarithm Series -- 3.6 Inequalities and Integrals -- 3.7 Generating Functions -- 3.8 Series with Harmonic and Skew-Harmonic Numbers -- 3.9 Remarkable Numerical and Function Series -- 3.10 Multiple Series with the Riemann Zeta Function -- 3.11 Series Involving Products of Harmonic Numbers -- 4 Derivatives and Applications -- 4.1 Apéritif -- 4.2 Integral Equations -- 4.3 Differential Equations -- 4.4 Higher Order Derivatives -- 4.5 Taylor's Formula -- 4.6 Series with the Maclaurin Remainder of a Function f -- 4.7 Series with Fractional Part Function -- 4.8 Extrema of One Variable Functions -- 5 Partial Derivatives and Applications -- 5.1 Partial Derivatives, the Jacobian and the Hessian Matrices, Differential Operators -- 5.2 The Chain Rule -- 5.3 Homogeneous Functions. Euler's Identity -- 5.4 Taylor's Formula for Real Functions of Two Real Variables -- 5.5 The Differential of "]
[{"$nulls":4},"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."]
[{"$nulls":4},"6.3 Implicit Functions of One Real Variable Defined by a System of Equations -- 6.4 Implicit Functions of Two Real Variables Defined by a System of Equations -- 7 Challenges, Gems, and Mathematical Beauties -- 7.1 Limits of Sequences -- 7.2 Limits of Integrals -- 7.3 Convergence and Evaluation of Series -- 7.4 Harmonic Series -- 7.5 Series with Factorials -- 7.6 Series of Functions -- 7.7 Pearls of Series with Tails of Zeta Function Values -- 7.8 Exotic Zeta Series -- 7.9 Special Differential Equations -- 7.10 Inequalities -- 7.11 Fabulous Integrals -- 8 An Artistry of Quadratic Series: Two New Proofs of Sandham-Yeung Series -- 8.1 The First Proof -- 8.2 The Second Proof -- Part II Solutions -- 9 Sequences of Real Numbers -- 9.1 Limits of Sequences -- 9.2 Applications of Stolz-Cesàro Theorem, the ∞/∞ and the 0/0 Cases -- 9.3 Wolstenholme Sequences -- 9.4 Limits of Integrals -- 10 Series of Real Numbers -- 10.1 Miscellaneous Series -- 10.2 Applications of Abel's Summation Formula -- 10.3 Series with Positive Terms -- 10.4 Alternating Series -- 10.5 Series with Harmonic Numbers and Factorials -- 10.6 A Mosaic of Series -- 11 Power Series -- 11.1 Convergence and Sum of Power Series -- 11.2 Maclaurin Series of Elementary Functions -- 11.3 Gems with Numerical and Power Series -- 11.4 Single Zeta Series -- 11.5 Polylogarithm Series -- 11.6 Inequalities and Integrals -- 11.7 Generating Functions -- 11.8 Series with Harmonic and Skew-Harmonic Numbers -- 11.9 Remarkable Numerical and Function Series -- 11.10 Multiple Series with the Riemann Zeta Function -- 11.11 Series Involving Products of Harmonic Numbers -- 12 Derivatives and Applications -- 12.1 Apéritif -- 12.2 Integral Equations -- 12.3 Differential Equations -- 12.4 Higher Order Derivatives -- 12.5 Taylor's Formula -- 12.6 Series with the Maclaurin Remainder of a Function f."]
[{"$nulls":4},"12.7 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."]