The divergence theorem and sets of finite perimeter (Record no. 15290)
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| fixed length control field | 03190cam a2200361Ia 4500 |
| 001 - CONTROL NUMBER | |
| control field | CAH0KE16167PDF |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | FlBoTFG |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20171224123559.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 120720s2012 flu sb 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781466507210 (ebook : PDF) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | FlBoTFG |
| Transcribing agency | FlBoTFG |
| 090 ## - LOCALLY ASSIGNED LC-TYPE CALL NUMBER (OCLC); LOCAL CALL NUMBER (OCLC) | |
| Classification number (OCLC) (R) ; Classification number, CALL (RLIN) (NR) | QA433 |
| Local cutter number (OCLC) ; Book number/undivided call number, CALL (RLIN) | .P493 2012 |
| 092 ## - LOCALLY ASSIGNED DEWEY CALL NUMBER (OCLC) | |
| Classification number | 515.4 |
| Item number | P524 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Pfeffer, Washek F. |
| 245 14 - TITLE STATEMENT | |
| Title | The divergence theorem and sets of finite perimeter |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | Washek F. Pfeffer. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Boca Raton : |
| Name of publisher, distributor, etc | CRC Press, |
| Date of publication, distribution, etc | 2012. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xv, 242 p. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Monographs and textbooks in pure and applied mathematics |
| 500 ## - GENERAL NOTE | |
| General note | "A Chapman & Hall book." |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references (p. 231-233) and index. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | pt. 1. Dyadic figures -- pt. 2. Sets of finite perimeter -- pt. 3. The divergence theorem. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | "Preface The divergence theorem and the resulting integration by parts formula belong to the most frequently used tools of mathematical analysis. In its elementary form, that is for smooth vector fields defined in a neighborhood of some simple geometric object such as rectangle, cylinder, ball, etc., the divergence theorem is presented in many calculus books. Its proof is obtained by a simple application of the one-dimensional fundamental theorem of calculus and iterated Riemann integration. Appreciable difficulties arise when we consider a more general situation. Employing the Lebesgue integral is essential, but it is only the first step in a long struggle. We divide the problem into three parts. (1) Extending the family of vector fields for which the divergence theorem holds on simple sets. (2) Extending the the family of sets for which the divergence theorem holds for Lipschitz vector fields. (3) Proving the divergence theorem when the vector fields and sets are extended simultaneously. Of these problems, part (2) is unquestionably the most complicated. While many mathematicians contributed to it, the Italian school represented by Caccioppoli, De Giorgi, and others, obtained a complete solution by defining the sets of bounded variation (BV sets). A major contribution to part (3) is due to Federer, who proved the divergence theorem for BV sets and Lipschitz vector fields. While parts (1)-(3) can be combined, treating them separately illuminates the exposition. We begin with sets that are locally simple: finite unions of dyadic cubes, called dyadic figures. Combining ideas of Henstock and McShane with a combinatorial argument of Jurkat, we establish the divergence theorem for very general vector fields defined on dyadic figures"-- |
| -- | Provided by publisher. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE | |
| Additional physical form available note | Also available in print edition. |
| 538 ## - SYSTEM DETAILS NOTE | |
| System details note | Mode of access: World Wide Web. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Divergence theorem. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Differential calculus. |
| 655 #7 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| Source of term | lcsh |
| 776 1# - ADDITIONAL PHYSICAL FORM ENTRY | |
| International Standard Book Number | 9781466507197 (hardback) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Monographs and textbooks in pure and applied mathematics. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://marc.crcnetbase.com/isbn/9781466507210 |
| Electronic format type | application/PDF |
| Public note | Distributed by publisher. Purchase or institutional license may be required for access. |
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