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Introduction to real analysis [[electronic resource] ] : an educational approach / / William C. Bauldry
| Introduction to real analysis [[electronic resource] ] : an educational approach / / William C. Bauldry |
| Autore | Bauldry William C |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2009 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina |
515
515.8 |
| Soggetto topico |
Mathematical analysis
Functions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-27392-6
9786613273925 1-118-16441-5 1-118-16443-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to Real Analysis: An Educational Approach; CONTENTS; Preface; Acknowledgments; 1 Elementary Calculus; 1.1 Preliminary Concepts; 1.2 Limits and Continuity; 1.3 Differentiation; 1.4 Integration; 1.5 Sequences and Series of Constants; 1.6 Power Series and Taylor Series; Summary; Exercises; Interlude: Fermat, Descartes, and the Tangent Problem; 2 Introduction to Real Analysis; 2.1 Basic Topology of the Real Numbers; 2.2 Limits and Continuity; 2.3 Differentiation; 2.4 Riemann and Riemann-Stieltjes Integration; 2.5 Sequences, Series, and Convergence Tests
2.6 Pointwise and Uniform ConvergenceSummary; Exercises; Interlude: Euler and the ""Basel Problem""; 3 A Brief Introduction to Lebesgue Theory; 3.1 Lebesgue Measure and Measurable Sets; 3.2 The Lebesgue Integral; 3.3 Measure, Integral, and Convergence; 3.4 Littlewood's Three Principles; Summary; Exercises; Interlude: The Set of Rational Numbers Is Very Large and Very Small; 4 Special Topics; 4.1 Modeling with Logistic Functions-Numerical Derivatives; 4.2 Numerical Quadrature; 4.3 Fourier Series; 4.4 Special Functions-The Gamma Function; 4.5 Calculus Without Limits: Differential Algebra SummaryExercises; Appendix A: Definitions & Theorems of Elementary Real Analysis; A.1 Limits; A.2 Continuity; A.3 The Derivative; A.4 Riemann Integration; A.5 Riemann-Stieltjes Integration; A.6 Sequences and Series of Constants; A.7 Sequences and Series of Functions; Appendix B: A Brief Calculus Chronology; Appendix C: Projects in Real Analysis; C.1 Historical Writing Projects; C.2 Induction Proofs: Summations, Inequalities, and Divisibility; C.3 Series Rearrangements; C.4 Newton and the Binomial Theorem; C.5 Symmetric Sums of Logarithms C.6 Logical Equivalence: Completeness of the Real NumbersC.7 Vitali's Nonmeasurable Set; C.8 Sources for Real Analysis Projects; C.9 Sources for Projects for Calculus Students; Bibliography; Index |
| Record Nr. | UNINA-9910139592803321 |
Bauldry William C
|
||
| Hoboken, N.J., : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to real analysis [[electronic resource] ] : an educational approach / / William C. Bauldry
| Introduction to real analysis [[electronic resource] ] : an educational approach / / William C. Bauldry |
| Autore | Bauldry William C |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2009 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina |
515
515.8 |
| Soggetto topico |
Mathematical analysis
Functions |
| ISBN |
1-283-27392-6
9786613273925 1-118-16441-5 1-118-16443-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to Real Analysis: An Educational Approach; CONTENTS; Preface; Acknowledgments; 1 Elementary Calculus; 1.1 Preliminary Concepts; 1.2 Limits and Continuity; 1.3 Differentiation; 1.4 Integration; 1.5 Sequences and Series of Constants; 1.6 Power Series and Taylor Series; Summary; Exercises; Interlude: Fermat, Descartes, and the Tangent Problem; 2 Introduction to Real Analysis; 2.1 Basic Topology of the Real Numbers; 2.2 Limits and Continuity; 2.3 Differentiation; 2.4 Riemann and Riemann-Stieltjes Integration; 2.5 Sequences, Series, and Convergence Tests
2.6 Pointwise and Uniform ConvergenceSummary; Exercises; Interlude: Euler and the ""Basel Problem""; 3 A Brief Introduction to Lebesgue Theory; 3.1 Lebesgue Measure and Measurable Sets; 3.2 The Lebesgue Integral; 3.3 Measure, Integral, and Convergence; 3.4 Littlewood's Three Principles; Summary; Exercises; Interlude: The Set of Rational Numbers Is Very Large and Very Small; 4 Special Topics; 4.1 Modeling with Logistic Functions-Numerical Derivatives; 4.2 Numerical Quadrature; 4.3 Fourier Series; 4.4 Special Functions-The Gamma Function; 4.5 Calculus Without Limits: Differential Algebra SummaryExercises; Appendix A: Definitions & Theorems of Elementary Real Analysis; A.1 Limits; A.2 Continuity; A.3 The Derivative; A.4 Riemann Integration; A.5 Riemann-Stieltjes Integration; A.6 Sequences and Series of Constants; A.7 Sequences and Series of Functions; Appendix B: A Brief Calculus Chronology; Appendix C: Projects in Real Analysis; C.1 Historical Writing Projects; C.2 Induction Proofs: Summations, Inequalities, and Divisibility; C.3 Series Rearrangements; C.4 Newton and the Binomial Theorem; C.5 Symmetric Sums of Logarithms C.6 Logical Equivalence: Completeness of the Real NumbersC.7 Vitali's Nonmeasurable Set; C.8 Sources for Real Analysis Projects; C.9 Sources for Projects for Calculus Students; Bibliography; Index |
| Record Nr. | UNINA-9910831196203321 |
|
Bauldry William C
|
||
| Hoboken, N.J., : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to real analysis : an educational approach / / William C. Bauldry
| Introduction to real analysis : an educational approach / / William C. Bauldry |
| Autore | Bauldry William C |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2009 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 515 |
| Soggetto topico |
Mathematical analysis
Functions |
| ISBN |
1-283-27392-6
9786613273925 1-118-16441-5 1-118-16443-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to Real Analysis: An Educational Approach; CONTENTS; Preface; Acknowledgments; 1 Elementary Calculus; 1.1 Preliminary Concepts; 1.2 Limits and Continuity; 1.3 Differentiation; 1.4 Integration; 1.5 Sequences and Series of Constants; 1.6 Power Series and Taylor Series; Summary; Exercises; Interlude: Fermat, Descartes, and the Tangent Problem; 2 Introduction to Real Analysis; 2.1 Basic Topology of the Real Numbers; 2.2 Limits and Continuity; 2.3 Differentiation; 2.4 Riemann and Riemann-Stieltjes Integration; 2.5 Sequences, Series, and Convergence Tests
2.6 Pointwise and Uniform ConvergenceSummary; Exercises; Interlude: Euler and the ""Basel Problem""; 3 A Brief Introduction to Lebesgue Theory; 3.1 Lebesgue Measure and Measurable Sets; 3.2 The Lebesgue Integral; 3.3 Measure, Integral, and Convergence; 3.4 Littlewood's Three Principles; Summary; Exercises; Interlude: The Set of Rational Numbers Is Very Large and Very Small; 4 Special Topics; 4.1 Modeling with Logistic Functions-Numerical Derivatives; 4.2 Numerical Quadrature; 4.3 Fourier Series; 4.4 Special Functions-The Gamma Function; 4.5 Calculus Without Limits: Differential Algebra SummaryExercises; Appendix A: Definitions & Theorems of Elementary Real Analysis; A.1 Limits; A.2 Continuity; A.3 The Derivative; A.4 Riemann Integration; A.5 Riemann-Stieltjes Integration; A.6 Sequences and Series of Constants; A.7 Sequences and Series of Functions; Appendix B: A Brief Calculus Chronology; Appendix C: Projects in Real Analysis; C.1 Historical Writing Projects; C.2 Induction Proofs: Summations, Inequalities, and Divisibility; C.3 Series Rearrangements; C.4 Newton and the Binomial Theorem; C.5 Symmetric Sums of Logarithms C.6 Logical Equivalence: Completeness of the Real NumbersC.7 Vitali's Nonmeasurable Set; C.8 Sources for Real Analysis Projects; C.9 Sources for Projects for Calculus Students; Bibliography; Index |
| Record Nr. | UNINA-9910878086303321 |
|
Bauldry William C
|
||
| Hoboken, N.J., : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||