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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 | ||
| ||
Lebesgue measure and integration [[electronic resource] ] : an introduction / / Frank Burk
| Lebesgue measure and integration [[electronic resource] ] : an introduction / / Frank Burk |
| Autore | Burk Frank |
| Pubbl/distr/stampa | New York, : Wiley, c1998 |
| Descrizione fisica | 1 online resource (314 p.) |
| Disciplina | 515/.42 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Lebesgue integral
Measure theory |
| ISBN |
1-283-30619-0
9786613306197 1-118-03273-X 1-118-03098-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910139571803321 |
|
Burk Frank
|
||
| New York, : Wiley, c1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lebesgue measure and integration [[electronic resource] ] : an introduction / / Frank Burk
| Lebesgue measure and integration [[electronic resource] ] : an introduction / / Frank Burk |
| Autore | Burk Frank |
| Pubbl/distr/stampa | New York, : Wiley, c1998 |
| Descrizione fisica | 1 online resource (314 p.) |
| Disciplina | 515/.42 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Lebesgue integral
Measure theory |
| ISBN |
1-283-30619-0
9786613306197 1-118-03273-X 1-118-03098-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910830529003321 |
|
Burk Frank
|
||
| New York, : Wiley, c1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lebesgue measure and integration : an introduction / / Frank Burk
| Lebesgue measure and integration : an introduction / / Frank Burk |
| Autore | Burk Frank |
| Pubbl/distr/stampa | New York, : Wiley, c1998 |
| Descrizione fisica | 1 online resource (314 p.) |
| Disciplina | 515/.42 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Lebesgue integral
Measure theory |
| ISBN |
1-283-30619-0
9786613306197 1-118-03273-X 1-118-03098-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910877238103321 |
|
Burk Frank
|
||
| New York, : Wiley, c1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||