《从克利福德代数到几何微积分》封面

从克利福德代数到几何微积分

Clifford Algebra to Geometric Calculus

David Hestenes、Garret Sobczyk · 初版 1984 年

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Hacker News 上怎么说

  • …但鉴于 @eigenspace 是一位物理学家,你想要找的(符号用法等)可能在这里:http://geocalc.clas.asu.edu/html/Evolution.html#References 在 “Recent Books” 下面。尤其是 Hestenes 写的《Clifford Algebra to Geometric Calculus》和《New Foundations for Classical Mechanics》。补充一句:如果你打算读这两本中的任何一本,我建议找最新(修正过的)重印本。

    …but given that @eigenspace is a physicist, what you are looking for (notations used, etc) is possibly here: http://geocalc.clas.asu.edu/html/Evolution.html#References under "Recent Books". Notably "Clifford Algebra to Geometric Calculus" and "New Foundations for Classical Mechanics" by Hestenes. PD: if you ever attempt to read any of those two, I'd advise to go to the latest (corrected) reprint.

  • …矩阵流形上的优化)4本计算机科学(亮点:CLRS 的《算法导论》)10本微积分/几何/拓扑/代数(亮点:Bachman 的微分形式几何方法、Hestenes & Sobzyk 的《Clifford algebra to geometric calculus》)8本小说写作(亮点:Bickham 的《Scene & Structure》)以及 Rosenberg 的《非暴力沟通》(Nonviolent Communication,虽不是教材,但仍是值得一提的亮点)。平均下来每年读 3 到 4 本。…

    …optimization on matrix manifolds) 4 on CS (highlight: CLRS’s intro to algorithms) 10 on calculus/geometry/topology/algebra (highlights: Bachman’s geometric approach to differential forms, Hestenes&Sobzyk's Clifford algebra to geometric calculus) 8 on fiction writing (highlight: Bickham’s Scene & Structure) And Rosenberg‘s Nonviolent Communication (not a textbook, but still a highlight worth mentioning). It amounts to between 3 and 4 per year.…

  • …揭示了电场和磁场之间的关系。我同意文章的观点,先不管它本身到底有多完美,它都会是一种教授新人物理学的好方法。我已经订了一本《Clifford Algebra to Geometric Calculus》。至于用它来做广义相对论或量子力学、甚至量子场论(Quantum Field Theory)的研究到底实不实用,就留给那些领域的专家来评判吧。作为一个外行…

    …revealing the relationship between electric and magnetic fields. I agree with the article that whatever its absolute merits, it would be a good way to teach new physicists. I have already ordered my copy of "Clifford Algebra to Geometric Calculus". Whether it is actually more practical to do work in General Relativity or Quantum Mechanics, or indeed Quantum Field Theory etc., I'll have to leave for the experts in those fields. From an outsider's…

  • …面向同类受众的其他书倒是不多。MacDonald 还有一本《Vector and Geometric Calculus》,我猜读起来会比 Hestenes 和 Sobczyk 的《Clifford Algebra to Geometric Calculus》轻松得多。(MacDonald 的两本书我都没看过)如果你对机器人学、计算机图形学、计算机视觉等领域的几何建模感兴趣,不妨看看[这些论文][invkinematics]…

    …not too much else pitched at a similar audience. MacDonald also has a book [Vector and Geometric Calculus][vagc] which I suspect will be substantially easier to work through than Hestenes and Sobczyk’s [Clifford Algebra to Geometric Calculus][cagc]. (I haven’t looked at either of MacDonald’s books) If you’re interested in geometric modeling for robotics, computer graphics, computer vision, or similar, check out [these papers][invkinematics]…

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