Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering (Record no. 55724)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05548cam a2200625Mu 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9780429343315 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | FlBoTFG |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220414100114.0 |
| 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 | 200912s2020 xx o 000 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | OCoLC-P |
| Language of cataloging | eng |
| Description conventions | pn |
| Transcribing agency | OCoLC-P |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781000205879 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1000205878 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781000205893 |
| Qualifying information | (ePub ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1000205894 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781000205886 |
| Qualifying information | (Mobipocket ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1000205886 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780429343315 |
| Qualifying information | (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0429343310 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780367356743 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 0367356740 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1201/9780429343315 |
| Source of number or code | doi |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1193130373 |
| Canceled/invalid control number | (OCoLC)1191239474 |
| -- | (OCoLC)1196191988 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC-P)1193130373 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA320 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 037000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | SCI |
| Subject category code subdivision | 040000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 000000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKF |
| Source | bicssc |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.64 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Botelho, Fabio Silva. |
| 245 10 - TITLE STATEMENT | |
| Title | Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
| Place of publication, distribution, etc. | Milton : |
| Name of publisher, distributor, etc. | Taylor & Francis Group, |
| Date of publication, distribution, etc. | 2020. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (589 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 336 ## - CONTENT TYPE | |
| Content type term | still image |
| Content type code | sti |
| 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 Page -- Copyright Page -- Preface -- Acknowledgements -- Table of Contents -- Section I: Functional Analysis -- 1. Metric Spaces -- 1.1 Introduction -- 1.2 The main definitions -- 1.2.1 The space l |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1.5 The Arzela-Ascoli theorem -- 2. Topological Vector Spaces -- 2.1 Introduction -- 2.2 Vector spaces -- 2.3 Some properties of topological vector spaces -- 2.3.1 Nets and convergence -- 2.4 Compactness in topological vector spaces -- 2.4.1 A note on convexity in topological vector spaces -- 2.5 Normed and metric spaces -- 2.6 Linear mappings -- 2.7 Linearity and continuity -- 2.8 Continuity of operators in Banach spaces -- 2.9 Some classical results on Banach spaces -- 2.9.1 The Baire Category theorem -- 2.9.2 The Principle of Uniform Boundedness -- 2.9.3 The Open Mapping theorem |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 2.9.4 The Closed Graph theorem -- 2.10 A note on finite dimensional normed spaces -- 3. Hilbert Spaces -- 3.1 Introduction -- 3.2 The main definitions and results -- 3.3 Orthonormal basis -- 3.3.1 The Gram-Schmidt orthonormalization -- 3.4 Projection on a convex set -- 3.5 The theorems of Stampacchia and Lax-Milgram -- 4. The Hahn-Banach Theorems and the Weak Topologies -- 4.1 Introduction -- 4.2 The Hahn-Banach theorems -- 4.3 The weak topologies -- 4.4 The weak-star topology -- 4.5 Weak-star compactness -- 4.6 Separable sets -- 4.7 Uniformly convex spaces -- 5. Topics on Linear Operators |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 5.1 Topologies for bounded operators -- 5.2 Adjoint operators -- 5.3 Compact operators -- 5.4 The square root of a positive operator -- 6. Spectral Analysis, a General Approach in Normed Spaces -- 6.1 Introduction -- 6.2 Sesquilinear functionals -- 6.3 About the spectrum of a linear operator defined on a banach space -- 6.4 The spectral theorem for bounded self-adjoint operators -- 6.4.1 The spectral theorem -- 6.5 The spectral decomposition of unitary transformations -- 6.6 Unbounded operators -- 6.6.1 Introduction -- 6.7 Symmetric and self-adjoint operators |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.7.1 The spectral theorem using Cayley transform -- 7. Basic Results on Measure and Integration -- 7.1 Basic concepts -- 7.2 Simple functions -- 7.3 Measures -- 7.4 Integration of simple functions -- 7.5 Signed measures -- 7.6 The Radon-Nikodym theorem -- 7.7 Outer measure and measurability -- 7.8 Fubini's theorem -- 7.8.1 Product measures -- 8. The Lebesgue Measure in Rn -- 8.1 Introduction -- 8.2 Properties of the outer measure -- 8.3 The Lebesgue measure -- 8.4 Outer and inner approximations of Lebesgue measurable sets -- 8.5 Some other properties of measurable sets |
| 500 ## - GENERAL NOTE | |
| General note | 8.6 Lebesgue measurable functions |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | OCLC-licensed vendor bibliographic record. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Calculus of variations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Functional analysis. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | MATHEMATICS |
| General subdivision | Functional Analysis. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | SCIENCE |
| General subdivision | Mathematical Physics. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | MATHEMATICS |
| General subdivision | General. |
| Source of heading or term | bisacsh |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | Taylor & Francis |
| Uniform Resource Identifier | <a href="https://www.taylorfrancis.com/books/e/9780429343315">https://www.taylorfrancis.com/books/e/9780429343315</a> |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | OCLC metadata license agreement |
| Uniform Resource Identifier | <a href="http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf">http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf</a> |
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