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Titlebook: Clifford Algebra to Geometric Calculus; A Unified Language f David Hestenes,Garret Sobczyk Book 1984 Springer Science+Business Media Dordre

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發(fā)表于 2025-3-21 17:04:13 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Clifford Algebra to Geometric Calculus
副標(biāo)題A Unified Language f
編輯David Hestenes,Garret Sobczyk
視頻videohttp://file.papertrans.cn/228/227342/227342.mp4
叢書名稱Fundamental Theories of Physics
圖書封面Titlebook: Clifford Algebra to Geometric Calculus; A Unified Language f David Hestenes,Garret Sobczyk Book 1984 Springer Science+Business Media Dordre
描述Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called ‘Clifford Algebra‘, though we prefer the name ‘Geometric Algebm‘ suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
出版日期Book 1984
關(guān)鍵詞Fundamental theorem of calculus; Vector space; algebra; derivative; differential equation; geometry; mathe
版次1
doihttps://doi.org/10.1007/978-94-009-6292-7
isbn_softcover978-90-277-2561-5
isbn_ebook978-94-009-6292-7Series ISSN 0168-1222 Series E-ISSN 2365-6425
issn_series 0168-1222
copyrightSpringer Science+Business Media Dordrecht 1984
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 22:08:28 | 只看該作者
板凳
發(fā)表于 2025-3-22 02:36:22 | 只看該作者
The Method of Mobiles,nifold and the definitions and notations for differentials and codifferentials established in Sections 4-1 and 4-3, and a couple of results from Chapter 4 are used without taking the trouble to rederive them by the method of this chapter.
地板
發(fā)表于 2025-3-22 07:13:27 | 只看該作者
5#
發(fā)表于 2025-3-22 11:06:47 | 只看該作者
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發(fā)表于 2025-3-22 16:05:30 | 只看該作者
Overall Conclusion and Discussion,defined on more general subsets of . called manifolds, and this will be considered in Chapter 4. But in the interest of simplicity, it is best to study calculus on linear spaces first. Calculus on more general manifolds involves differential geometry.
7#
發(fā)表于 2025-3-22 20:13:57 | 只看該作者
Differentiation,defined on more general subsets of . called manifolds, and this will be considered in Chapter 4. But in the interest of simplicity, it is best to study calculus on linear spaces first. Calculus on more general manifolds involves differential geometry.
8#
發(fā)表于 2025-3-22 21:27:49 | 只看該作者
https://doi.org/10.1007/978-94-007-5527-7e generated by a few simple techniques. For example, Section 1-4 shows how easily geometric algebra generates the system of identities making up the theory of determinants. Thus we can see the theory of determinants as only part of a more comprehensive algebraic system.
9#
發(fā)表于 2025-3-23 04:48:35 | 只看該作者
https://doi.org/10.1007/3-540-59007-2re new, but our main objective is to demonstrate the unique advantages of the method and to develop the calculus to the point where application to any problem in differential geometry is straightforward.
10#
發(fā)表于 2025-3-23 07:46:15 | 只看該作者
https://doi.org/10.1007/3-540-59007-2nifold and the definitions and notations for differentials and codifferentials established in Sections 4-1 and 4-3, and a couple of results from Chapter 4 are used without taking the trouble to rederive them by the method of this chapter.
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