Ellipsoidal harmonics: theory and applications
The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in r...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2012
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 146 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xvi, 458 pages) |
| ISBN: | 9781139017749 |
| DOI: | 10.1017/CBO9781139017749 |
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| 505 | 8 | |a Prologue -- The ellipsoidal system and its geometry -- Differential operators in ellipsoidal geometry -- Lamé functions -- Ellipsoidal harmonics -- The theory of Niven and Cartesian harmonics -- Integration techniques -- Boundary value problems in ellipsoidal geometry -- Connection between harmonics -- The elliptic functions approach -- Ellipsoidal biharmonic functions -- Vector ellipsoidal harmonics -- Applications to geometry -- Applications to physics -- Applications to low-frequency scattering theory -- Applications to bioscience -- Applications to inverse problems -- Epilogue -- Appendix A. Background material -- Appendix B. Elements of dyadic analysis -- Appendix C. Legendre functions and spherical harmonics -- Appendix D. The fundamental polyadic integral -- Appendix E. Forms of the Lamé equation -- Appendix F. Table of formulae -- Appendix G. Miscellaneous relations | |
| 520 | |a The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject | ||
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Datensatz im Suchindex
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| author | Dassios, G. |
| author_facet | Dassios, G. |
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| contents | Prologue -- The ellipsoidal system and its geometry -- Differential operators in ellipsoidal geometry -- Lamé functions -- Ellipsoidal harmonics -- The theory of Niven and Cartesian harmonics -- Integration techniques -- Boundary value problems in ellipsoidal geometry -- Connection between harmonics -- The elliptic functions approach -- Ellipsoidal biharmonic functions -- Vector ellipsoidal harmonics -- Applications to geometry -- Applications to physics -- Applications to low-frequency scattering theory -- Applications to bioscience -- Applications to inverse problems -- Epilogue -- Appendix A. Background material -- Appendix B. Elements of dyadic analysis -- Appendix C. Legendre functions and spherical harmonics -- Appendix D. The fundamental polyadic integral -- Appendix E. Forms of the Lamé equation -- Appendix F. Table of formulae -- Appendix G. Miscellaneous relations |
| ctrlnum | (ZDB-20-CBO)CR9781139017749 (OCoLC)852513678 (DE-599)BVBBV043942184 |
| dewey-full | 515/.53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.53 |
| dewey-search | 515/.53 |
| dewey-sort | 3515 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139017749 |
| format | Electronic eBook |
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| id | DE-604.BV043942184 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139017749 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351153 |
| oclc_num | 852513678 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xvi, 458 pages) |
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| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge University Press |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Dassios, G. Verfasser aut Ellipsoidal harmonics theory and applications George Dassios, University of Patras, Greece Cambridge Cambridge University Press 2012 1 online resource (xvi, 458 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 146 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Prologue -- The ellipsoidal system and its geometry -- Differential operators in ellipsoidal geometry -- Lamé functions -- Ellipsoidal harmonics -- The theory of Niven and Cartesian harmonics -- Integration techniques -- Boundary value problems in ellipsoidal geometry -- Connection between harmonics -- The elliptic functions approach -- Ellipsoidal biharmonic functions -- Vector ellipsoidal harmonics -- Applications to geometry -- Applications to physics -- Applications to low-frequency scattering theory -- Applications to bioscience -- Applications to inverse problems -- Epilogue -- Appendix A. Background material -- Appendix B. Elements of dyadic analysis -- Appendix C. Legendre functions and spherical harmonics -- Appendix D. The fundamental polyadic integral -- Appendix E. Forms of the Lamé equation -- Appendix F. Table of formulae -- Appendix G. Miscellaneous relations The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject Lamé's functions Erscheint auch als Druckausgabe 978-0-521-11309-0 https://doi.org/10.1017/CBO9781139017749 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Dassios, G. Ellipsoidal harmonics theory and applications Prologue -- The ellipsoidal system and its geometry -- Differential operators in ellipsoidal geometry -- Lamé functions -- Ellipsoidal harmonics -- The theory of Niven and Cartesian harmonics -- Integration techniques -- Boundary value problems in ellipsoidal geometry -- Connection between harmonics -- The elliptic functions approach -- Ellipsoidal biharmonic functions -- Vector ellipsoidal harmonics -- Applications to geometry -- Applications to physics -- Applications to low-frequency scattering theory -- Applications to bioscience -- Applications to inverse problems -- Epilogue -- Appendix A. Background material -- Appendix B. Elements of dyadic analysis -- Appendix C. Legendre functions and spherical harmonics -- Appendix D. The fundamental polyadic integral -- Appendix E. Forms of the Lamé equation -- Appendix F. Table of formulae -- Appendix G. Miscellaneous relations Lamé's functions |
| title | Ellipsoidal harmonics theory and applications |
| title_auth | Ellipsoidal harmonics theory and applications |
| title_exact_search | Ellipsoidal harmonics theory and applications |
| title_full | Ellipsoidal harmonics theory and applications George Dassios, University of Patras, Greece |
| title_fullStr | Ellipsoidal harmonics theory and applications George Dassios, University of Patras, Greece |
| title_full_unstemmed | Ellipsoidal harmonics theory and applications George Dassios, University of Patras, Greece |
| title_short | Ellipsoidal harmonics |
| title_sort | ellipsoidal harmonics theory and applications |
| title_sub | theory and applications |
| topic | Lamé's functions |
| topic_facet | Lamé's functions |
| url | https://doi.org/10.1017/CBO9781139017749 |
| work_keys_str_mv | AT dassiosg ellipsoidalharmonicstheoryandapplications |