Symmetry Analysis of Differential Equations with Mathematica:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2000
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica 3.0 note books. The entire printed version of this book is available on the accompanying CD. The text is presented in such a way that the reader can interact with the calculations and experiment with the models and methods. Also contained on the CD is a package called MathLie- in honor of Sophus Lie- carrying out the calculations automatically. The application of symmetry analysis to problems from physics, mathematics, and engineering is demonstrated by many examples. The study of symmetries of differential equations is an old subject. Thanks to Sophus Lie we today have available to us important information on the behavior of differential equations. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. They can provide conservation laws for differential equations. The theory presented here is based on Lie, containing improvements and generalizations made by later mathematicians who rediscovered and used Lie's work. The presentation of Lie's theory in connection with Mathematica is novel and vitalizes an old theory. The extensive symbolic calculations necessary under Lie's theory are supported by MathLie, a package written in Mathematica |
| Beschreibung: | 1 Online-Ressource (XII, 521 p) |
| ISBN: | 9781461221104 9781461274186 |
| DOI: | 10.1007/978-1-4612-2110-4 |
Internformat
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| 500 | |a The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica 3.0 note books. The entire printed version of this book is available on the accompanying CD. The text is presented in such a way that the reader can interact with the calculations and experiment with the models and methods. Also contained on the CD is a package called MathLie- in honor of Sophus Lie- carrying out the calculations automatically. The application of symmetry analysis to problems from physics, mathematics, and engineering is demonstrated by many examples. The study of symmetries of differential equations is an old subject. Thanks to Sophus Lie we today have available to us important information on the behavior of differential equations. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. They can provide conservation laws for differential equations. The theory presented here is based on Lie, containing improvements and generalizations made by later mathematicians who rediscovered and used Lie's work. The presentation of Lie's theory in connection with Mathematica is novel and vitalizes an old theory. The extensive symbolic calculations necessary under Lie's theory are supported by MathLie, a package written in Mathematica | ||
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Datensatz im Suchindex
| _version_ | 1804153091309699072 |
|---|---|
| any_adam_object | |
| author | Baumann, Gerd |
| author_facet | Baumann, Gerd |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2110-4 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
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| isbn | 9781461221104 9781461274186 |
| language | English |
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| spelling | Baumann, Gerd Verfasser aut Symmetry Analysis of Differential Equations with Mathematica by Gerd Baumann New York, NY Springer New York 2000 1 Online-Ressource (XII, 521 p) txt rdacontent c rdamedia cr rdacarrier The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica 3.0 note books. The entire printed version of this book is available on the accompanying CD. The text is presented in such a way that the reader can interact with the calculations and experiment with the models and methods. Also contained on the CD is a package called MathLie- in honor of Sophus Lie- carrying out the calculations automatically. The application of symmetry analysis to problems from physics, mathematics, and engineering is demonstrated by many examples. The study of symmetries of differential equations is an old subject. Thanks to Sophus Lie we today have available to us important information on the behavior of differential equations. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. They can provide conservation laws for differential equations. The theory presented here is based on Lie, containing improvements and generalizations made by later mathematicians who rediscovered and used Lie's work. The presentation of Lie's theory in connection with Mathematica is novel and vitalizes an old theory. The extensive symbolic calculations necessary under Lie's theory are supported by MathLie, a package written in Mathematica Mathematics Chemistry / Mathematics Algebra Numerical analysis Mathematical physics Engineering mathematics Numerical Analysis Mathematical Methods in Physics Numerical and Computational Physics Math. Applications in Chemistry Appl.Mathematics/Computational Methods of Engineering Chemie Mathematik Mathematische Physik Symmetrie (DE-588)4058724-1 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Symmetrie (DE-588)4058724-1 s Mathematica Programm (DE-588)4268208-3 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-2110-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Baumann, Gerd Symmetry Analysis of Differential Equations with Mathematica Mathematics Chemistry / Mathematics Algebra Numerical analysis Mathematical physics Engineering mathematics Numerical Analysis Mathematical Methods in Physics Numerical and Computational Physics Math. Applications in Chemistry Appl.Mathematics/Computational Methods of Engineering Chemie Mathematik Mathematische Physik Symmetrie (DE-588)4058724-1 gnd Mathematica Programm (DE-588)4268208-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4268208-3 (DE-588)4012249-9 |
| title | Symmetry Analysis of Differential Equations with Mathematica |
| title_auth | Symmetry Analysis of Differential Equations with Mathematica |
| title_exact_search | Symmetry Analysis of Differential Equations with Mathematica |
| title_full | Symmetry Analysis of Differential Equations with Mathematica by Gerd Baumann |
| title_fullStr | Symmetry Analysis of Differential Equations with Mathematica by Gerd Baumann |
| title_full_unstemmed | Symmetry Analysis of Differential Equations with Mathematica by Gerd Baumann |
| title_short | Symmetry Analysis of Differential Equations with Mathematica |
| title_sort | symmetry analysis of differential equations with mathematica |
| topic | Mathematics Chemistry / Mathematics Algebra Numerical analysis Mathematical physics Engineering mathematics Numerical Analysis Mathematical Methods in Physics Numerical and Computational Physics Math. Applications in Chemistry Appl.Mathematics/Computational Methods of Engineering Chemie Mathematik Mathematische Physik Symmetrie (DE-588)4058724-1 gnd Mathematica Programm (DE-588)4268208-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematics Chemistry / Mathematics Algebra Numerical analysis Mathematical physics Engineering mathematics Numerical Analysis Mathematical Methods in Physics Numerical and Computational Physics Math. Applications in Chemistry Appl.Mathematics/Computational Methods of Engineering Chemie Mathematik Mathematische Physik Symmetrie Mathematica Programm Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4612-2110-4 |
| work_keys_str_mv | AT baumanngerd symmetryanalysisofdifferentialequationswithmathematica |