The divergence and curl in arbitrary basis
محفوظ في:
| المؤلف الرئيسي: | |
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| تاريخ النشر: | 2019 |
| مؤلفون آخرون: | , , |
| التنسيق: | Article |
| اللغة: | eng |
| المصدر: | Repositório Institucional da UnB |
| Download full: | https://repositorio.unb.br/handle/10482/36550 https://doi.org/10.1590/1806-9126-rbef-2018-0082 http://orcid.org/0000-0003-4650-5947 |
الملخص: | In this work, the divergence and curl operators are obtained using the coordinate free non rigid basis formulation of differential geometry. Although the authors have attempted to keep the presentation self-contained as much as possible, some previous exposure to the language of differential geometry may be helpful. In this sense the work is aimed to late undergraduate or beginners graduate students interested in mathematical physics. To illustrate the development, we graphically present the eleven coordinate systems in which the Laplace operator is separable. We detail the development of the basis and the connection for the cylindrical and paraboloidal coordinate systems. We also present in [1] codes both in Maxima and Maple for the spherical orthonormal basis, which serves as a working model for calculations in other situations of interest. Also in [1] the codes to obtain the coordinate surfaces are given. |
مواد مشابهة: The divergence and curl in arbitrary basis
- Aplicações do estudo do cálculo integral no nível básico de ensino associado à resolução do cálculo de áreas de figuras planas
- Translação e rotação de cônicas em R²
- Análise não linear de pórticos planos utilizando uma formulação co-rotacional e plasticidade por camadas
- The computation of pitch with vectors
- Avaliação para aprendizagem na disciplina de Cálculo 1 : percepções de discentes e docentes da Universidade de Brasília
- Sobre o processo ensino-aprendizagem do cálculo infinitesimal