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The elements of integration and Lebesgue measure / / Robert G. Bartle
| The elements of integration and Lebesgue measure / / Robert G. Bartle |
| Autore | Bartle Robert Gardner <1927-> |
| Edizione | [Wiley classics library ed.] |
| Pubbl/distr/stampa | New York, : Wiley, 1995 |
| Descrizione fisica | 1 online resource (194 p.) |
| Disciplina | 515/.43 |
| Collana | Wiley classics library |
| Soggetto topico |
Integrals, Generalized
Measure theory |
| ISBN |
1-283-27394-2
9786613273949 1-118-16447-4 1-118-16448-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The Elements of Integration and Lebesgue Measure; Contents; The Elements of Integration; 1. Introduction; 2. Measurable Functions; 3. Measures; 4. The Integral; 5. Integrable Functions; 6. The Lebesgue Spaces Lp; 7. Modes of Convergence; 8. Decomposition of Measures; 9. Generation of Measures; 10. Product Measures; The Elements of Lebesgue Measure; 11. Volumes of Cells and Intervals; 12. The Outer Measure; 13. Measurable Sets; 14. Examples of Measurable Sets; 15. Approximation of Measurable Sets; 16. Additivity and Nonadditivity; 17. Nonmeasurable and Non-Borel Sets; References; Index |
| Record Nr. | UNINA-9911020025903321 |
Bartle Robert Gardner <1927->
|
||
| New York, : Wiley, 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A garden of integrals [[electronic resource] /] / Frank E. Burk
| A garden of integrals [[electronic resource] /] / Frank E. Burk |
| Autore | Burk Frank |
| Pubbl/distr/stampa | Washington, D.C., : Mathematical Association of America, c2007 |
| Descrizione fisica | 1 online resource (xiv, 281 pages) : digital, PDF file(s) |
| Disciplina | 515/.43 |
| Collana | Dolciani mathematical expositions |
| Soggetto topico | Integrals |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-61444-209-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword -- ; An historical overview -- ; 1.1. Rearrangements -- ; 1.2. The lune of Hippocrates -- ; 1.3. Exodus and the method of exhaustion -- ; 1.4. Archimedes' method -- 1.5. Gottfried Leibniz and Isaac Newton -- ; 1.6. Augustin-Louis Cauchy -- ; 1.7. Bernhard Riemann -- ; 1.8. Thomas Stieltjes -- ; 1.9. Henri Lebesgue -- ; 1.10. The Lebesgue-Stieltjes integral -- ; 1.11. Ralph Henstock and Jaroslav Kurzweil -- ; 1.12. Norbert Wiener -- ; 1.13. Richard Feynman -- ; 1.14. References -- ; 2. The Cauchy integral -- ; 2.1. Exploring integration -- ; 2.2. Cauchy's integral -- ; 2.3. Recovering functions by integration -- ; 2.4. Recovering functions by differentiation -- ; 2.5. A convergence theorem -- ; 2.6. Joseph Fourier -- ; 2.7. P.G. Lejeune Dirichlet -- ; 2.8. Patrick Billingsley's example -- ; 2.9. Summary -- ; 2.10. References -- ; 3. The Riemann integral -- ; 3.1. Riemann's integral -- ; 3.2. Criteria for Riemann integrability -- ; 3.3. Cauchy and Darboux criteria for Riemann integrability -- ; 3.4. Weakening continuity -- ; 3.5. Monotonic functions are Riemann integrable -- ; 3.6. Lebesgue's criteria -- ; 3.7. Evaluating à la Riemann -- ; 3.8. Sequences of Riemann integrable functions -- ; 3.9. The Cantor set -- ; 3.10. A nowhere dense set of positive measure -- ; 3.11. Cantor functions -- ; 3.12. Volterra's example -- ; 3.13. Lengths of graphs and the Cantor function -- ; 3.14. Summary -- ; 3.15. References.
; 4. Riemann-Stieltjes integral -- ; 4.1. Generalizing the Riemann integral-- ; 4.2. Discontinuities -- ; 4.3. Existence of Riemann-Stieltjes integrals -- ; 4.4. Monotonicity of [null] -- ; 4.5. Euler's summation formula -- ; 4.6. Uniform convergence and R-S integration -- ; 4.7. References -- ; 5. Lebesgue measure -- ; 5.1. Lebesgue's idea -- ; 5.2. Measurable sets -- ; 5.3. Lebesgue measurable sets and Carathéodory -- ; 5.4. Sigma algebras -- ; 5.5. Borel sets -- ; 5.6. Approximating measurable sets -- ; 5.7. Measurable functions -- ; 5.8. More measureable functions -- ; 5.9. What does monotonicity tell us? -- ; 5.10. Lebesgue's differentiation theorem -- ; 5.11. References -- ; 6. The Lebesgue-Stieltjes integral -- ; 6.1. Introduction -- ; 6.2. Integrability : Riemann ensures Lebesgue -- ; 6.3. Convergence theorems -- ; 6.4. Fundamental theorems for the Lebesgue integral -- ; 6.5. Spaces -- ; 6.6. L²[-pi, pi] and Fourier series -- ; 6.7. Lebesgue measure in the plane and Fubini's theorem -- ; 6.8. Summary-- References -- ; 7. The Lebesgue-Stieltjes integral -- ; 7.1. L-S measures and monotone increasing functions -- ; 7.2. Carathéodory's measurability criterion -- ; 7.3. Avoiding complacency -- ; 7.4. L-S measures and nonnegative Lebesgue integrable functions -- ; 7.5. L-S measures and random variables -- ; 7.6. The Lebesgue-Stieltjes integral -- ; 7.7. A fundamental theorem for L-S integrals -- ; 7.8. References. ; 8. The Henstock-Kurzweil integral -- ; 8.1. The generalized Riemann integral -- ; 8.2. Gauges and [infinity]-fine partitions -- ; 8.3. H-K integrable functions -- ; 8.4. The Cauchy criterion for H-K integrability -- ; 8.5. Henstock's lemma -- ; 8.6. Convergence theorems for the H-K integral -- ; 8.7. Some properties of the H-K integral -- ; 8.8. The second fundamental theorem -- ; 8.9. Summary-- ; 8.10. References -- ; 9. The Wiener integral -- ; 9.1. Brownian motion -- ; 9.2. Construction of the Wiener measure -- ; 9.3. Wiener's theorem -- ; 9.4. Measurable functionals -- ; 9.5. The Wiener integral -- ; 9.6. Functionals dependent on a finite number of t values -- ; 9.7. Kac's theorem -- ; 9.8. References -- ; 10. Feynman integral -- ; 10.1. Introduction -- ; 10.2. Summing probability amplitudes -- ; 10.3. A simple example -- ; 10.4. The Fourier transform -- ; 10.5. The convolution product -- ; 10.6. The Schwartz space -- ; 10.7. Solving Schrödinger problem A -- ; 10.8. An abstract Cauchy problem -- ; 10.9. Solving in the Schwartz space -- ; 10.10. Solving Schrödinger problem B -- ; 10.11. References -- Index -- About the author. |
| Record Nr. | UNINA-9910465210903321 |
|
Burk Frank
|
||
| Washington, D.C., : Mathematical Association of America, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A garden of integrals / / Frank Burk [[electronic resource]]
| A garden of integrals / / Frank Burk [[electronic resource]] |
| Autore | Burk Frank |
| Pubbl/distr/stampa | Washington : , : Mathematical Association of America, , 2007 |
| Descrizione fisica | 1 online resource (xiv, 281 pages) : digital, PDF file(s) |
| Disciplina | 515/.43 |
| Collana |
Dolciani Mathematical Expositions
Dolciani mathematical expositions |
| Soggetto topico | Integrals |
| ISBN | 1-61444-209-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword -- ; An historical overview -- ; 1.1. Rearrangements -- ; 1.2. The lune of Hippocrates -- ; 1.3. Exdoxus and the method of exhaustion -- ; 1.4. Archimedes' method -- 1.5. Gottfried Leibniz and Isaac Newton -- ; 1.6. Augustin-Louis Cauchy -- ; 1.7. Bernhard Riemann -- ; 1.8. Thomas Stieltjes -- ; 1.9. Henri Lebesgue -- ; 1.10. The Lebesgue-Stieltjes integral -- ; 1.11. Ralph Henstock and Jaroslav Kurzweil -- ; 1.12. Norbert Wiener -- ; 1.13. Richard Feynman -- ; 1.14. References -- ; 2. The Cauchy integral -- ; 2.1. Exploring integration -- ; 2.2. Cauchy's integral -- ; 2.3. Recovering functions by integration -- ; 2.4. Recovering functions by differentiation -- ; 2.5. A convergence theorem -- ; 2.6. Joseph Fourier -- ; 2.7. P.G. Lejeune Dirichlet -- ; 2.8. Patrick Billingsley's example -- ; 2.9. Summary -- ; 2.10. References -- ; 3. The Riemann integral -- ; 3.1. Riemann's integral -- ; 3.2. Criteria for Riemann integrability -- ; 3.3. Cauchy and Darboux criteria for Riemann integrability -- ; 3.4. Weakening continuity -- ; 3.5. Monotonic functions are Riemann integrable -- ; 3.6. Lebesgue's criteria -- ; 3.7. Evaluating à la Riemann -- ; 3.8. Sequences of Riemann integrable functions -- ; 3.9. The Cantor set -- ; 3.10. A nowhere dense set of positive measure -- ; 3.11. Cantor functions -- ; 3.12. Volterra's example -- ; 3.13. Lengths of graphs and the Cantor function -- ; 3.14. Summary -- ; 3.15. References.
; 4. Riemann-Stieltjes integral -- ; 4.1. Generalizing the Riemann integral-- ; 4.2. Discontinuities -- ; 4.3. Existence of Riemann-Stieltjes integrals -- ; 4.4. Monotonicity of [null] -- ; 4.5. Euler's summation formula -- ; 4.6. Uniform convergence and R-S integration -- ; 4.7. References -- ; 5. Lebesgue measure -- ; 5.1. Lebesgue's idea -- ; 5.2. Measurable sets -- ; 5.3. Lebesgue measurable sets and Carathéodory -- ; 5.4. Sigma algebras -- ; 5.5. Borel sets -- ; 5.6. Approximating measurable sets -- ; 5.7. Measurable functions -- ; 5.8. More measureable functions -- ; 5.9. What does monotonicity tell us? -- ; 5.10. Lebesgue's differentiation theorem -- ; 5.11. References -- ; 6. The Lebesgue-Stieltjes integral -- ; 6.1. Introduction -- ; 6.2. Integrability : Riemann ensures Lebesgue -- ; 6.3. Convergence theorems -- ; 6.4. Fundamental theorems for the Lebesgue integral -- ; 6.5. Spaces -- ; 6.6. L²[-pi, pi] and Fourier series -- ; 6.7. Lebesgue measure in the plane and Fubini's theorem -- ; 6.8. Summary-- References -- ; 7. The Lebesgue-Stieltjes integral -- ; 7.1. L-S measures and monotone increasing functions -- ; 7.2. Carathéodory's measurability criterion -- ; 7.3. Avoiding complacency -- ; 7.4. L-S measures and nonnegative Lebesgue integrable functions -- ; 7.5. L-S measures and random variables -- ; 7.6. The Lebesgue-Stieltjes integral -- ; 7.7. A fundamental theorem for L-S integrals -- ; 7.8. References. ; 8. The Henstock-Kurzweil integral -- ; 8.1. The generalized Riemann integral -- ; 8.2. Gauges and [infinity]-fine partitions -- ; 8.3. H-K integrable functions -- ; 8.4. The Cauchy criterion for H-K integrability -- ; 8.5. Henstock's lemma -- ; 8.6. Convergence theorems for the H-K integral -- ; 8.7. Some properties of the H-K integral -- ; 8.8. The second fundamental theorem -- ; 8.9. Summary-- ; 8.10. References -- ; 9. The Wiener integral -- ; 9.1. Brownian motion -- ; 9.2. Construction of the Wiener measure -- ; 9.3. Wiener's theorem -- ; 9.4. Measurable functionals -- ; 9.5. The Wiener integral -- ; 9.6. Functionals dependent on a finite number of t values -- ; 9.7. Kac's theorem -- ; 9.8. References -- ; 10. Feynman integral -- ; 10.1. Introduction -- ; 10.2. Summing probability amplitudes -- ; 10.3. A simple example -- ; 10.4. The Fourier transform -- ; 10.5. The convolution product -- ; 10.6. The Schwartz space -- ; 10.7. Solving Schrödinger problem A -- ; 10.8. An abstract Cauchy problem -- ; 10.9. Solving in the Schwartz space -- ; 10.10. Solving Schrödinger problem B -- ; 10.11. References -- Index -- About the author. |
| Record Nr. | UNINA-9910791746803321 |
|
Burk Frank
|
||
| Washington : , : Mathematical Association of America, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A garden of integrals / / Frank Burk [[electronic resource]]
| A garden of integrals / / Frank Burk [[electronic resource]] |
| Autore | Burk Frank |
| Pubbl/distr/stampa | Washington : , : Mathematical Association of America, , 2007 |
| Descrizione fisica | 1 online resource (xiv, 281 pages) : digital, PDF file(s) |
| Disciplina | 515/.43 |
| Collana |
Dolciani Mathematical Expositions
Dolciani mathematical expositions |
| Soggetto topico | Integrals |
| ISBN | 1-61444-209-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword -- ; An historical overview -- ; 1.1. Rearrangements -- ; 1.2. The lune of Hippocrates -- ; 1.3. Exdoxus and the method of exhaustion -- ; 1.4. Archimedes' method -- 1.5. Gottfried Leibniz and Isaac Newton -- ; 1.6. Augustin-Louis Cauchy -- ; 1.7. Bernhard Riemann -- ; 1.8. Thomas Stieltjes -- ; 1.9. Henri Lebesgue -- ; 1.10. The Lebesgue-Stieltjes integral -- ; 1.11. Ralph Henstock and Jaroslav Kurzweil -- ; 1.12. Norbert Wiener -- ; 1.13. Richard Feynman -- ; 1.14. References -- ; 2. The Cauchy integral -- ; 2.1. Exploring integration -- ; 2.2. Cauchy's integral -- ; 2.3. Recovering functions by integration -- ; 2.4. Recovering functions by differentiation -- ; 2.5. A convergence theorem -- ; 2.6. Joseph Fourier -- ; 2.7. P.G. Lejeune Dirichlet -- ; 2.8. Patrick Billingsley's example -- ; 2.9. Summary -- ; 2.10. References -- ; 3. The Riemann integral -- ; 3.1. Riemann's integral -- ; 3.2. Criteria for Riemann integrability -- ; 3.3. Cauchy and Darboux criteria for Riemann integrability -- ; 3.4. Weakening continuity -- ; 3.5. Monotonic functions are Riemann integrable -- ; 3.6. Lebesgue's criteria -- ; 3.7. Evaluating à la Riemann -- ; 3.8. Sequences of Riemann integrable functions -- ; 3.9. The Cantor set -- ; 3.10. A nowhere dense set of positive measure -- ; 3.11. Cantor functions -- ; 3.12. Volterra's example -- ; 3.13. Lengths of graphs and the Cantor function -- ; 3.14. Summary -- ; 3.15. References.
; 4. Riemann-Stieltjes integral -- ; 4.1. Generalizing the Riemann integral-- ; 4.2. Discontinuities -- ; 4.3. Existence of Riemann-Stieltjes integrals -- ; 4.4. Monotonicity of [null] -- ; 4.5. Euler's summation formula -- ; 4.6. Uniform convergence and R-S integration -- ; 4.7. References -- ; 5. Lebesgue measure -- ; 5.1. Lebesgue's idea -- ; 5.2. Measurable sets -- ; 5.3. Lebesgue measurable sets and Carathéodory -- ; 5.4. Sigma algebras -- ; 5.5. Borel sets -- ; 5.6. Approximating measurable sets -- ; 5.7. Measurable functions -- ; 5.8. More measureable functions -- ; 5.9. What does monotonicity tell us? -- ; 5.10. Lebesgue's differentiation theorem -- ; 5.11. References -- ; 6. The Lebesgue-Stieltjes integral -- ; 6.1. Introduction -- ; 6.2. Integrability : Riemann ensures Lebesgue -- ; 6.3. Convergence theorems -- ; 6.4. Fundamental theorems for the Lebesgue integral -- ; 6.5. Spaces -- ; 6.6. L²[-pi, pi] and Fourier series -- ; 6.7. Lebesgue measure in the plane and Fubini's theorem -- ; 6.8. Summary-- References -- ; 7. The Lebesgue-Stieltjes integral -- ; 7.1. L-S measures and monotone increasing functions -- ; 7.2. Carathéodory's measurability criterion -- ; 7.3. Avoiding complacency -- ; 7.4. L-S measures and nonnegative Lebesgue integrable functions -- ; 7.5. L-S measures and random variables -- ; 7.6. The Lebesgue-Stieltjes integral -- ; 7.7. A fundamental theorem for L-S integrals -- ; 7.8. References. ; 8. The Henstock-Kurzweil integral -- ; 8.1. The generalized Riemann integral -- ; 8.2. Gauges and [infinity]-fine partitions -- ; 8.3. H-K integrable functions -- ; 8.4. The Cauchy criterion for H-K integrability -- ; 8.5. Henstock's lemma -- ; 8.6. Convergence theorems for the H-K integral -- ; 8.7. Some properties of the H-K integral -- ; 8.8. The second fundamental theorem -- ; 8.9. Summary-- ; 8.10. References -- ; 9. The Wiener integral -- ; 9.1. Brownian motion -- ; 9.2. Construction of the Wiener measure -- ; 9.3. Wiener's theorem -- ; 9.4. Measurable functionals -- ; 9.5. The Wiener integral -- ; 9.6. Functionals dependent on a finite number of t values -- ; 9.7. Kac's theorem -- ; 9.8. References -- ; 10. Feynman integral -- ; 10.1. Introduction -- ; 10.2. Summing probability amplitudes -- ; 10.3. A simple example -- ; 10.4. The Fourier transform -- ; 10.5. The convolution product -- ; 10.6. The Schwartz space -- ; 10.7. Solving Schrödinger problem A -- ; 10.8. An abstract Cauchy problem -- ; 10.9. Solving in the Schwartz space -- ; 10.10. Solving Schrödinger problem B -- ; 10.11. References -- Index -- About the author. |
| Record Nr. | UNINA-9910814891603321 |
|
Burk Frank
|
||
| Washington : , : Mathematical Association of America, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Improper Riemann integrals / / Ioannis M. Roussos, Hamline University, Saint Paul, Minnesota, USA
| Improper Riemann integrals / / Ioannis M. Roussos, Hamline University, Saint Paul, Minnesota, USA |
| Autore | Roussos Ioannis Markos |
| Pubbl/distr/stampa | Boca Raton, [Florida] : , : CRC/Taylor & Francis, , [2014] |
| Descrizione fisica | 1 online resource (681 p.) |
| Disciplina |
515.43
515/.43 |
| Soggetto topico | Riemann integral |
| ISBN |
0-429-16833-0
1-4665-8807-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cover; Contents; Acknowledgements; Prologue; Chapter 1: Improper Riemann Integrals; Chapter 2: Real Analysis Techniques; Chapter 3: Complex Analysis Techniques; Chapter 4: List of Non-elementary Integrals and Sums in Text; Bibliography; Back Cover |
| Record Nr. | UNINA-9910787577203321 |
|
Roussos Ioannis Markos
|
||
| Boca Raton, [Florida] : , : CRC/Taylor & Francis, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Improper Riemann integrals / / Ioannis M. Roussos, Hamline University, Saint Paul, Minnesota, USA
| Improper Riemann integrals / / Ioannis M. Roussos, Hamline University, Saint Paul, Minnesota, USA |
| Autore | Roussos Ioannis Markos |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Boca Raton, [Florida] : , : CRC/Taylor & Francis, , [2014] |
| Descrizione fisica | 1 online resource (681 p.) |
| Disciplina |
515.43
515/.43 |
| Soggetto topico | Riemann integral |
| ISBN |
1-04-021272-7
0-429-16833-0 1-4665-8807-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cover; Contents; Acknowledgements; Prologue; Chapter 1: Improper Riemann Integrals; Chapter 2: Real Analysis Techniques; Chapter 3: Complex Analysis Techniques; Chapter 4: List of Non-elementary Integrals and Sums in Text; Bibliography; Back Cover |
| Record Nr. | UNINA-9910971988903321 |
|
Roussos Ioannis Markos
|
||
| Boca Raton, [Florida] : , : CRC/Taylor & Francis, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to gauge integrals [[electronic resource] /] / Charles Swartz
| Introduction to gauge integrals [[electronic resource] /] / Charles Swartz |
| Autore | Swartz Charles <1938-> |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (150p.) |
| Disciplina | 515/.43 |
| Soggetto topico |
Henstock-Kurzweil integral
Calculus |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-95631-7
9786611956318 981-281-065-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction to the gauge or Henstock-Kurzweil integral; basic properties of the gauge integral; Henstock's Lemma and improper integrals; the gauge integral over unbounded intervals; convergence theorems; integration over more general sets -Lebesgue measure; the space of gauge integrable functions; multiple integrals and Fubini's theorem; the McShane integral; McShane integrability is equivalent to absolute Henstock-Kurzweil integrability. |
| Record Nr. | UNINA-9910453187603321 |
|
Swartz Charles <1938->
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to gauge integrals [[electronic resource] /] / Charles Swartz
| Introduction to gauge integrals [[electronic resource] /] / Charles Swartz |
| Autore | Swartz Charles <1938-> |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (150p.) |
| Disciplina | 515/.43 |
| Soggetto topico |
Henstock-Kurzweil integral
Calculus |
| ISBN |
1-281-95631-7
9786611956318 981-281-065-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction to the gauge or Henstock-Kurzweil integral; basic properties of the gauge integral; Henstock's Lemma and improper integrals; the gauge integral over unbounded intervals; convergence theorems; integration over more general sets -Lebesgue measure; the space of gauge integrable functions; multiple integrals and Fubini's theorem; the McShane integral; McShane integrability is equivalent to absolute Henstock-Kurzweil integrability. |
| Record Nr. | UNINA-9910782276903321 |
|
Swartz Charles <1938->
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to integral calculus [[electronic resource] ] : systematic studies with engineering applications for beginners / / Ulrich L. Rohde ... [et al.]
| Introduction to integral calculus [[electronic resource] ] : systematic studies with engineering applications for beginners / / Ulrich L. Rohde ... [et al.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2012 |
| Descrizione fisica | 1 online resource (430 p.) |
| Disciplina | 515/.43 |
| Altri autori (Persone) | RohdeUlrich L |
| Soggetto topico | Calculus, Integral |
| ISBN |
1-283-40084-7
9786613400840 1-118-13034-0 1-118-13033-2 1-118-13031-6 |
| Classificazione | SK 400 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to Integral Calculus: Systematic Studies with Engineering Applications for Beginners; CONTENTS; FOREWORD; PREFACE; BIOGRAPHIES; INTRODUCTION; ACKNOWLEDGMENT; 1 Antiderivative(s) [or Indefinite Integral(s)]; 1.1 Introduction; 1.2 Useful Symbols, Terms, and Phrases Frequently Needed; 1.3 Table(s) of Derivatives and their corresponding Integrals; 1.4 Integration of Certain Combinations of Functions; 1.5 Comparison Between the Operations of Differentiation and Integration; 2 Integration Using Trigonometric Identities; 2.1 Introduction
2.2 Some Important Integrals Involving sin x and cos x2.3 Integrals of the Form B;(dx/(asin x + b cosx)), where a, Є r; 3a Integration by Substitution: Change of Variable of Integration; 3a.1 Introduction; 3a.2 Generalized Power Rule; 3a.3 Theorem; 3a.4 To Evaluate Integrals of the Form B; a sin x + b cos x/c sin x + d cos x dx; where a, b, c, and d are constant; 3b Further Integration by Substitution: Additional Standard Integrals; 3b.1 Introduction; 3b.2 Special Cases of Integrals and Proof for Standard Integrals; 3b.3 Some New Integrals; 3b.4 Four More Standard Integrals 4a Integration by Parts 4a.1 Introduction; 4a.2 Obtaining the Rule for Integration by Parts; 4a.3 Helpful Pictures Connecting Inverse Trigonometric Functions with Ordinary Trigonometric Functions; 4a.4 Rule for Proper Choice of First Function; 4b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side; 4b.1 Introduction; 4b.2 An Important Result: A Corollary to Integration by Parts; 4b.3 Application of the Corollary to Integration by Parts to Integrals that cannot be Solved Otherwise; 4b.4 Simpler Method(s) for Evaluating Standard Integrals 4b.5 To Evaluate x2 + bx + cdx5 Preparation for the Definite Integral: The Concept of Area; 5.1 Introduction; 5.2 Preparation for the Definite Integral; 5.3 The Definite Integral as an Area; 5.4 Definition of Area in Terms of the Definite Integral; 5.5 Riemann Sums and the Analytical Definition of the Definite Integral; 6a The Fundamental Theorems of Calculus; 6a.1 Introduction; 6a.2 Definite Integrals; 6a.3 The Area of Function A(x); 6a.4 Statement and Proof of the Second Fundamental Theorem of Calculus; 6a.5 Differentiating a Definite Integral with Respect to a Variable Upper Limit 6b The Integral Function x1 1/ t dt, (x > 0) Identified as ln x or logex 6b.1 Introduction; 6b.2 Definition of Natural Logarithmic Function; 6b.3 The Calculus of ln x; 6b.4 The Graph of the Natural Logarithmic Function ln x; 6b.5 The Natural Exponential Function [exp(x) or ex]; 7a Methods for Evaluating Definite Integrals; 7a.1 Introduction; 7a.2 The Rule for Evaluating Definite Integrals; 7a.3 Some Rules (Theorems) for Evaluation of Definite Integrals; 7a.4 Method of Integration by Parts in Definite Integrals; 7b Some Important Properties of Definite Integrals; 7b.1 Introduction 7b.2 Some Important Properties of Definite Integrals |
| Record Nr. | UNINA-9910141174603321 |
| Hoboken, N.J., : Wiley, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to integral calculus : systematic studies with engineering applications for beginners / / Ulrich L. Rohde ... [et al.]
| Introduction to integral calculus : systematic studies with engineering applications for beginners / / Ulrich L. Rohde ... [et al.] |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2012 |
| Descrizione fisica | 1 online resource (430 p.) |
| Disciplina | 515/.43 |
| Altri autori (Persone) | RohdeUlrich L |
| Soggetto topico | Calculus, Integral |
| ISBN |
9786613400840
9781283400848 1283400847 9781118130346 1118130340 9781118130339 1118130332 9781118130315 1118130316 |
| Classificazione | SK 400 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to Integral Calculus: Systematic Studies with Engineering Applications for Beginners; CONTENTS; FOREWORD; PREFACE; BIOGRAPHIES; INTRODUCTION; ACKNOWLEDGMENT; 1 Antiderivative(s) [or Indefinite Integral(s)]; 1.1 Introduction; 1.2 Useful Symbols, Terms, and Phrases Frequently Needed; 1.3 Table(s) of Derivatives and their corresponding Integrals; 1.4 Integration of Certain Combinations of Functions; 1.5 Comparison Between the Operations of Differentiation and Integration; 2 Integration Using Trigonometric Identities; 2.1 Introduction
2.2 Some Important Integrals Involving sin x and cos x2.3 Integrals of the Form B;(dx/(asin x + b cosx)), where a, Є r; 3a Integration by Substitution: Change of Variable of Integration; 3a.1 Introduction; 3a.2 Generalized Power Rule; 3a.3 Theorem; 3a.4 To Evaluate Integrals of the Form B; a sin x + b cos x/c sin x + d cos x dx; where a, b, c, and d are constant; 3b Further Integration by Substitution: Additional Standard Integrals; 3b.1 Introduction; 3b.2 Special Cases of Integrals and Proof for Standard Integrals; 3b.3 Some New Integrals; 3b.4 Four More Standard Integrals 4a Integration by Parts 4a.1 Introduction; 4a.2 Obtaining the Rule for Integration by Parts; 4a.3 Helpful Pictures Connecting Inverse Trigonometric Functions with Ordinary Trigonometric Functions; 4a.4 Rule for Proper Choice of First Function; 4b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side; 4b.1 Introduction; 4b.2 An Important Result: A Corollary to Integration by Parts; 4b.3 Application of the Corollary to Integration by Parts to Integrals that cannot be Solved Otherwise; 4b.4 Simpler Method(s) for Evaluating Standard Integrals 4b.5 To Evaluate x2 + bx + cdx5 Preparation for the Definite Integral: The Concept of Area; 5.1 Introduction; 5.2 Preparation for the Definite Integral; 5.3 The Definite Integral as an Area; 5.4 Definition of Area in Terms of the Definite Integral; 5.5 Riemann Sums and the Analytical Definition of the Definite Integral; 6a The Fundamental Theorems of Calculus; 6a.1 Introduction; 6a.2 Definite Integrals; 6a.3 The Area of Function A(x); 6a.4 Statement and Proof of the Second Fundamental Theorem of Calculus; 6a.5 Differentiating a Definite Integral with Respect to a Variable Upper Limit 6b The Integral Function x1 1/ t dt, (x > 0) Identified as ln x or logex 6b.1 Introduction; 6b.2 Definition of Natural Logarithmic Function; 6b.3 The Calculus of ln x; 6b.4 The Graph of the Natural Logarithmic Function ln x; 6b.5 The Natural Exponential Function [exp(x) or ex]; 7a Methods for Evaluating Definite Integrals; 7a.1 Introduction; 7a.2 The Rule for Evaluating Definite Integrals; 7a.3 Some Rules (Theorems) for Evaluation of Definite Integrals; 7a.4 Method of Integration by Parts in Definite Integrals; 7b Some Important Properties of Definite Integrals; 7b.1 Introduction 7b.2 Some Important Properties of Definite Integrals |
| Record Nr. | UNINA-9910824313703321 |
| Hoboken, N.J., : Wiley, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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