A garden of integrals:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Washington, DC
Mathematical Association of America
c2007
|
Schriftenreihe: | Dolciani mathematical expositions
no. 31 |
Schlagworte: | |
Online-Zugang: | FAW01 FAW02 Volltext |
Beschreibung: | Includes bibliographical references and index 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 |
Beschreibung: | 1 Online-Ressource (xiv, 281 p.) |
ISBN: | 088385337X 1614442096 9780883853375 9781614442097 |
Internformat
MARC
LEADER | 00000nmm a2200000zcb4500 | ||
---|---|---|---|
001 | BV043171434 | ||
003 | DE-604 | ||
005 | 00000000000000.0 | ||
007 | cr|uuu---uuuuu | ||
008 | 151126s2007 |||| o||u| ||||||eng d | ||
020 | |a 088385337X |9 0-88385-337-X | ||
020 | |a 1614442096 |9 1-61444-209-6 | ||
020 | |a 9780883853375 |9 978-0-88385-337-5 | ||
020 | |a 9781614442097 |9 978-1-61444-209-7 | ||
035 | |a (OCoLC)793207766 | ||
035 | |a (DE-599)BVBBV043171434 | ||
040 | |a DE-604 |b ger |e aacr | ||
041 | 0 | |a eng | |
049 | |a DE-1046 |a DE-1047 | ||
082 | 0 | |a 515/.43 |2 22 | |
100 | 1 | |a Burk, Frank |e Verfasser |4 aut | |
245 | 1 | 0 | |a A garden of integrals |c Frank Burk |
264 | 1 | |a Washington, DC |b Mathematical Association of America |c c2007 | |
300 | |a 1 Online-Ressource (xiv, 281 p.) | ||
336 | |b txt |2 rdacontent | ||
337 | |b c |2 rdamedia | ||
338 | |b cr |2 rdacarrier | ||
490 | 0 | |a Dolciani mathematical expositions |v no. 31 | |
500 | |a Includes bibliographical references and index | ||
500 | |a 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 -- | ||
500 | |a 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 -- | ||
500 | |a 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 | ||
650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
650 | 7 | |a Integrals |2 fast | |
650 | 4 | |a Integrals | |
650 | 0 | 7 | |a Integral |0 (DE-588)4131477-3 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Reelle Funktion |0 (DE-588)4048918-8 |2 gnd |9 rswk-swf |
689 | 0 | 0 | |a Reelle Funktion |0 (DE-588)4048918-8 |D s |
689 | 0 | 1 | |a Integral |0 (DE-588)4131477-3 |D s |
689 | 0 | |8 1\p |5 DE-604 | |
700 | 1 | |a Scully, Terence |e Sonstige |4 oth | |
856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282 |x Aggregator |3 Volltext |
912 | |a ZDB-4-EBA | ||
999 | |a oai:aleph.bib-bvb.de:BVB01-028595625 | ||
883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext |
Datensatz im Suchindex
_version_ | 1804175651995910144 |
---|---|
any_adam_object | |
author | Burk, Frank |
author_facet | Burk, Frank |
author_role | aut |
author_sort | Burk, Frank |
author_variant | f b fb |
building | Verbundindex |
bvnumber | BV043171434 |
collection | ZDB-4-EBA |
ctrlnum | (OCoLC)793207766 (DE-599)BVBBV043171434 |
dewey-full | 515/.43 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515/.43 |
dewey-search | 515/.43 |
dewey-sort | 3515 243 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Electronic eBook |
fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06264nmm a2200541zcb4500</leader><controlfield tag="001">BV043171434</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151126s2007 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">088385337X</subfield><subfield code="9">0-88385-337-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1614442096</subfield><subfield code="9">1-61444-209-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780883853375</subfield><subfield code="9">978-0-88385-337-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781614442097</subfield><subfield code="9">978-1-61444-209-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)793207766</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043171434</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.43</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Burk, Frank</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A garden of integrals</subfield><subfield code="c">Frank Burk</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Washington, DC</subfield><subfield code="b">Mathematical Association of America</subfield><subfield code="c">c2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xiv, 281 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Dolciani mathematical expositions</subfield><subfield code="v">no. 31</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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 --</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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 --</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Calculus</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Mathematical Analysis</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Integrals</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integrals</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reelle Funktion</subfield><subfield code="0">(DE-588)4048918-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Reelle Funktion</subfield><subfield code="0">(DE-588)4048918-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Scully, Terence</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028595625</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
id | DE-604.BV043171434 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T07:19:41Z |
institution | BVB |
isbn | 088385337X 1614442096 9780883853375 9781614442097 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028595625 |
oclc_num | 793207766 |
open_access_boolean | |
owner | DE-1046 DE-1047 |
owner_facet | DE-1046 DE-1047 |
physical | 1 Online-Ressource (xiv, 281 p.) |
psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
publishDate | 2007 |
publishDateSearch | 2007 |
publishDateSort | 2007 |
publisher | Mathematical Association of America |
record_format | marc |
series2 | Dolciani mathematical expositions |
spelling | Burk, Frank Verfasser aut A garden of integrals Frank Burk Washington, DC Mathematical Association of America c2007 1 Online-Ressource (xiv, 281 p.) txt rdacontent c rdamedia cr rdacarrier Dolciani mathematical expositions no. 31 Includes bibliographical references and index 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 MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Integrals fast Integrals Integral (DE-588)4131477-3 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 s Integral (DE-588)4131477-3 s 1\p DE-604 Scully, Terence Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Burk, Frank A garden of integrals MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Integrals fast Integrals Integral (DE-588)4131477-3 gnd Reelle Funktion (DE-588)4048918-8 gnd |
subject_GND | (DE-588)4131477-3 (DE-588)4048918-8 |
title | A garden of integrals |
title_auth | A garden of integrals |
title_exact_search | A garden of integrals |
title_full | A garden of integrals Frank Burk |
title_fullStr | A garden of integrals Frank Burk |
title_full_unstemmed | A garden of integrals Frank Burk |
title_short | A garden of integrals |
title_sort | a garden of integrals |
topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Integrals fast Integrals Integral (DE-588)4131477-3 gnd Reelle Funktion (DE-588)4048918-8 gnd |
topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Integrals Integral Reelle Funktion |
url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=450282 |
work_keys_str_mv | AT burkfrank agardenofintegrals AT scullyterence agardenofintegrals |