When least is best : (Record no. 81514)
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| fixed length control field | 06108cam a2200613 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | on1245418636 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220908100230.0 |
| 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 ||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 210323r20212004njua fo 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UKAHL |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UKAHL |
| Modifying agency | EBLCP |
| -- | JSTOR |
| -- | OCLCO |
| -- | OCLCF |
| -- | DEGRU |
| -- | IEEEE |
| -- | N$T |
| -- | ORZ |
| -- | OCLCO |
| -- | P@U |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0691220387 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780691220383 |
| Qualifying information | (electronic book) |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000069302854 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1245418636 |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 22573/ctv19qcvr2 |
| Source of stock number/acquisition | JSTOR |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 9519813 |
| Source of stock number/acquisition | IEEE |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA306 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 015000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511.66 |
| -- | 511/.66 |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Nahin, Paul J., |
| Relator term | author. |
| 9 (RLIN) | 65814 |
| 245 10 - TITLE STATEMENT | |
| Title | When least is best : |
| Remainder of title | how mathematicians discovered many clever ways to make things as small (or as large) as possible / |
| Statement of responsibility, etc. | Paul J. Nahin. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Princeton, New Jersey : |
| Name of producer, publisher, distributor, manufacturer | Princeton University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2021. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource : |
| Other physical details | illustrations |
| 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 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title -- Copyright -- Dedication -- Contents -- Preface to the 2021 Edition -- Preface to the 2007 Paperback Edition -- Preface -- 1. Minimums, Maximums, Derivatives, and Computers -- 1.1 Introduction -- 1.2 When Derivatives Don't Work -- 1.3 Using Algebra to Find Minimums -- 1.4 A Civil Engineering Problem -- 1.5 The AM-GM Inequality -- 1.6 Derivatives from Physics -- 1.7 Minimizing with a Computer -- 2. The First Extremal Problems -- 2.1 The Ancient Confusion of Length and Area -- 2.2 Dido's Problem and the Isoperimetric Quotient -- 2.3 Steiner's "Solution" to Dido's Problem |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 2.4 How Steiner Stumbled -- 2.5 A "Hard" Problem with an Easy Solution -- 2.6 Fagnano's Problem -- 3. Medieval Maximization and Some Modern Twists -- 3.1 The Regiomontanus Problem -- 3.2 The Saturn Problem -- 3.3 The Envelope-Folding Problem -- 3.4 The Pipe-and-Corner Problem -- 3.5 Regiomontanus Redux -- 3.6 The Muddy Wheel Problem -- 4. The Forgotten War of Descartes and Fermat -- 4.1 Two Very Different Men -- 4.2 Snell's Law -- 4.3 Fermat, Tangent Lines, and Extrema -- 4.4 The Birth of the Derivative -- 4.5 Derivatives and Tangents -- 4.6 Snell's Law and the Principle of Least Time |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.7 A Popular Textbook Problem -- 4.8 Snell's Law and the Rainbow -- 5. Calculus Steps Forward, Center Stage -- 5.1 The Derivative: Controversy and Triumph -- 5.2 Paintings Again, and Kepler's Wine Barrel -- 5.3 The Mailable Package Paradox -- 5.4 Projectile Motion in a Gravitational Field -- 5.5 The Perfect Basketball Shot -- 5.6 Halley's Gunnery Problem -- 5.7 De L'Hospital and His Pulley Problem, and a New Minimum Principle -- 5.8 Derivatives and the Rainbow -- 6. Beyond Calculus -- 6.1 Galileo's Problem -- 6.2 The Brachistochrone Problem -- 6.3 Comparing Galileo and Bernoulli |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.4 The Euler-Lagrange Equation -- 6.5 The Straight Line and the Brachistochrone -- 6.6 Galileo's Hanging Chain -- 6.7 The Catenary Again -- 6.8 The Isoperimetric Problem, Solved (at last!) -- 6.9 Minimal Area Surfaces, Plateau's Problem, and Soap Bubbles -- 6.10 The Human Side of Minimal Area Surfaces -- 7. The Modern Age Begins -- 7.1 The Fermat/Steiner Problem -- 7.2 Digging the Optimal Trench, Paving the Shortest Mail Route, and Least-Cost Paths through Directed Graphs -- 7.3 The Traveling Salesman Problem -- 7.4 Minimizing with Inequalities (Linear Programming) |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 7.5 Minimizing by Working Backwards (Dynamic Programming) -- Appendix A. The AM-GM Inequality -- Appendix B. The AM-QM Inequality, and Jensen's Inequality -- Appendix C. "The Sagacity of the Bees" -- Appendix D. Every Convex Figure Has a Perimeter Bisector -- Appendix E. The Gravitational Free-Fall Descent Time along a Circle -- Appendix F. The Area Enclosed by a Closed Curve -- Appendix G. Beltrami's Identity -- Appendix H. The Last Word on the Lost Fisherman Problem -- Appendix I. Solution to the New Challenge Problem -- Acknowledgments -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | A mathematical journey through the most fascinating problems of extremes and how to solve them. What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes--with values becoming as small (or as large) as possible--and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | IEEE |
| Provenance (VM) [OBSOLETE] | IEEE Xplore Princeton University Press eBooks Library |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Maxima and minima. |
| 9 (RLIN) | 65815 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Mathematics |
| General subdivision | History. |
| 9 (RLIN) | 63890 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Maximums et minimums. |
| 9 (RLIN) | 65816 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Math�ematiques |
| General subdivision | Histoire. |
| 9 (RLIN) | 63893 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | MATHEMATICS / History & Philosophy |
| Source of heading or term | bisacsh |
| 9 (RLIN) | 65248 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Mathematics. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst01012163 |
| 9 (RLIN) | 11584 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Maxima and minima. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst01012616 |
| 9 (RLIN) | 65815 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 9 (RLIN) | 3294 |
| 655 #7 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | History. |
| Source of term | fast |
| Authority record control number or standard number | (OCoLC)fst01411628 |
| 9 (RLIN) | 5289 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ieeexplore.ieee.org/servlet/opac?bknumber=9519813">https://ieeexplore.ieee.org/servlet/opac?bknumber=9519813</a> |
| 938 ## - | |
| -- | Project MUSE |
| -- | MUSE |
| -- | musev2_102044 |
| 938 ## - | |
| -- | De Gruyter |
| -- | DEGR |
| -- | 9780691220383 |
| 938 ## - | |
| -- | ProQuest Ebook Central |
| -- | EBLB |
| -- | EBL6534440 |
| 938 ## - | |
| -- | Askews and Holts Library Services |
| -- | ASKH |
| -- | AH38450360 |
| 938 ## - | |
| -- | EBSCOhost |
| -- | EBSC |
| -- | 2683325 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 994 ## - | |
| -- | 92 |
| -- | INTKS |
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