Garden of Integrals. (Record no. 79828)
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| 000 -LEADER | |
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| fixed length control field | 08400nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3330374 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729125049.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2007 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781614442097 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780883853375 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3330374 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3330374 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr10728523 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)929120469 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA308 -- .B868 2007eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.43 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Burk, Frank E. |
| 245 10 - TITLE STATEMENT | |
| Title | Garden of Integrals. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Washington : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2007. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2007. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (296 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Dolciani Mathematical Expositions ; |
| Volume/sequential designation | v.31 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- copyright page -- title page -- Foreword -- Contents -- 1 An Historical Overview -- 1.1 Rearrangements -- 1.2 The Lune of Hippocrates -- 1.3 Eudoxus and the Method of Exhaustion -- 1.4 Archimedes' Method -- 1.5 Gottfried Leibniz and Isaac Newton -- 1.5.1 Leibniz's Argument -- 1.5.2 Newton's Result -- 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 -- 2.1.1 Fermat's Formula -- 2.1.2 Wallis's Formula -- 2.1.3 Stirling's Formula -- 2.1.4 Stieltjes' Formula -- 2.2 Cauchy's Integral -- 2.2.1 Cauchy's Theorem (1823) -- 2.2.2 Cauchy Criteria for Cauchy Integrability -- 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 a la Riemann -- 3.8 Sequences of Riemann Integrable Functions -- 3.9 The Cantor Set (1883) -- 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 The Riemann{Stieltjes Integral -- 4.1 Generalizing the Riemann Integral -- 4.2 Discontinuities -- 4.3 Existence of Riemann{Stieltjes Integrals -- 4.4 Monotonicity of phi -- 4.5 Euler's Summation Formula. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.6 Uniform Convergence and R-S Integration -- 4.7 References -- 5 Lebesgue Measure -- 5.1 Lebesgue's Idea -- 5.2 Measurable Sets -- 5.2.1 The Wish List and Lebesgue Outer Measure -- 5.3 Lebesgue Measurable Sets and Carathéodory -- 5.4 Sigma Algebras -- 5.5 Borel Sets -- 5.6 Approximating Measurable Sets -- 5.6.1 Vitali's Covering Theorem -- 5.7 Measurable Functions -- 5.7.1 Continuous Functions Defined on Measurable Sets -- 5.7.2 Riemann Integrable Functions -- 5.7.3 Limiting Operations and Measurability -- 5.7.4 Simple Functions -- 5.7.5 Pointwise Convergence Is Almost Uniform Convergence -- 5.8 More Measureable Functions -- 5.8.1 Functions of Bounded Variation -- 5.8.2 Functions of Bounded Variation and Monotone Functions -- 5.8.3 Absolutely Continuous Functions -- 5.9 What Does Monotonicity Tell Us? -- 5.9.1 Dini Derivates of a Function -- 5.10 Lebesgue's Differentiation Theorem -- 5.11 References -- 6 The Lebesgue Integral -- 6.1 Introduction -- 6.1.1 Lebesgue's Integral -- 6.1.2 Young's Approach -- 6.1.3 And Another Approach -- 6.2 Integrability: Riemann Ensures Lebesgue -- 6.2.1 Nonnegative Unbounded Measurable Functions -- 6.2.2 Positive and Negative Measurable Functions -- 6.2.3 Arbitrary Measurable Subsets -- 6.2.4 Another Definition of the Lebesgue Integral -- 6.3 Convergence Theorems -- 6.3.1 Monotone Convergence -- 6.3.2 Sequential Convergence -- 6.3.3 The Dominated Convergence Theorem -- 6.3.4 Interchanging summation and Integral -- 6.4 Fundamental Theorems for the Lebesgue Integral -- 6.4.1 Properties of the Indefinite Integral -- 6.4.2 A Fundamental Theorem for the Lebesgue Integral -- 6.4.3 The Other Fundamental Theorem -- 6.4.4 The Bounded Variation Condition -- 6.4.5 Another Fundamental Theorem of Calculus -- 6.4.6 Comments -- 6.5 Spaces -- 6.5.1 Metric Space -- 6.5.2 Famous Inequalities -- 6.5.3 Completeness. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.5.4 The Riesz Completeness Theorem -- 6.6 L^2 [- pi, pi] and Fourier Series -- 6.7 Lebesgue Measure in the Plane and Fubini's Theorem -- 6.8 Summary -- 6.9 References -- 7 The Lebesgue{Stieltjes Integral -- 7.1 L-S Measures and Monotone Increasing Functions -- 7.1.1 Properties of the Weight Function -- 7.1.2 The L-S Outer Measure -- 7.2 Carathe odory's Measurability Criterion -- 7.3 Avoiding Complacency -- 7.4 L-S Measures and Nonnegative Lebesgue Integrable Functions -- 7.4.1 Properties of mu_f -- 7.5 L-S Measures and Random Variables -- 7.5.1 Properties of F_X -- 7.6 The Lebesgue{Stieltjes Integral -- 7.7 A Fundamental Theorem for L-S Integrals -- 7.8 Reference -- 8 The Henstock{Kurzweil Integral -- 8.1 The Generalized Riemann Integral -- 8.2 Gauges and delta-fine Partitions -- 8.3 H-K Integrable Functions -- 8.3.2 Riemann 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 -- 8.6.1 Monotone Convergence -- 8.6.2 Dominated Convergence -- 8.7 Some Properties of the H-K Integral -- 8.7.1 Extension of Lebesgue -- 8.7.2 Recovering Functions via Differentiation -- 8.7.3 H-K, but not Lebesgue, Integrable -- 8.7.4 Fundamental H-K Theorem -- 8.7.5 Sawtooth Functions -- 8.8 The Second Fundamental Theorem -- 8.8.1 Some H-K Properties -- 8.8.2 Second Fundamental Theorem for H-K -- 8.9 Summary -- 8.10 References -- 9 The Wiener Integral -- 9.1 Brownian Motion -- 9.1.1 Wiener's Explanation -- 9.2 Construction of the Wiener Measure -- 9.2.1 Borel Cylinders with One Restriction -- 9.2.2 Borel Cylinders with Two Restrictions -- 9.2.3 The Sigma Algebra B^[0.1] -- 9.3 Wiener's Theorem -- 9.3.1 Open Sets and Open Balls -- 9.4 Measurable Functionals -- 9.5 The Wiener Integral -- 9.6 Functionals Dependent on a Finite Number of t Values -- 9.6.1 More Interesting Functionals. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 9.7 Kac's Theorem -- 9.8 References -- 10 The Feynman Integral -- 10.1 Introduction -- 10.1.1 Schrödinger's Equation -- 10.1.2 Feynman's Riemann Sums -- 10.2 Summing Probability Amplitudes -- 10.2.1 First Approximation -- 10.2.2 Second Approximation -- 10.2.3 The Normalizing Constant -- 10.3 A Simple Example -- 10.4 The Fourier Transform -- 10.5 The Convolution Product -- 10.6 The Schwartz Space -- 10.6.1 Plancherel's Theorem -- 10.7 Solving SchroŁ dinger Problem A -- 10.7.1 Finding the Right Space of Functions -- 10.8 An Abstract Cauchy Problem -- 10.8.1 Defining the Abstract Cauchy Problem -- 10.8.2 Operators on a Complex Hilbert Space -- 10.9 Solving in the Schwartz Space -- 10.9.1 Extending the Solution of Problem A -- 10.9.2 A Theorem -- 10.10 Solving Schrödinger Problem B -- 10.10.1 Prelude to Problem B -- 10.10.2 Trotter's Contribution -- 10.10.3 Semigroups of Linear Operators -- 10.10.4 Semigroup Terminology and a Theorem -- 10.10.5 Some Notes on Our Solution -- 10.10.6 Applying the Theorem -- 10.10.7 Problem B and the Trotter Product -- 10.11 References -- Index -- About the Author. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Integrals. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Burk, Frank E. |
| Title | Garden of Integrals |
| Place, publisher, and date of publication | Washington : American Mathematical Society,c2007 |
| International Standard Book Number | 9780883853375 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Dolciani Mathematical Expositions |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330374">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330374</a> |
| Public note | Click to View |
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