散度、梯度、旋度及一切
Div, grad, curl, and all that
H. M. Schey · 初版 1973 年
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为什么值得读
- 仅约一百二十页，能迅速建立扎实的三维直觉
- 语言通俗非正式，是理解麦克斯韦方程的捷径
- 极大降低工程学与本科向量微积分的学习难度
引言、向量函数与静电学 —— 面积分与散度 —— 线积分与旋度 —— 梯度。
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Div, grad, curl, and all that
H. M. Schey · 初版 1973 年
引言、向量函数与静电学 —— 面积分与散度 —— 线积分与旋度 —— 梯度。
正在加载完整评论……
《Div, Grad, Curl, And All That: An Informal Text On Vector Calculus》（散度、旋度、梯度及其他：向量微积分通俗读本）这是我在布朗大学读本科微积分时的一本“选读”书，全班大概只有我一个人真的抽空读了它，而它让我后来的大部分工程课学起来轻松得飞起……
"Div, Grad, Curl, And All That: An Informal Text On Vector Calculus" This was "optional" reading in my Undergrad Calculus class at Brown, I probably was the only student who bothered to read it, and it made most of engineering a breeze…
……如果要推荐书的话，我脑海中首先浮现的是：- 格里菲斯（Griffiths）的《量子力学导论》[0]。它已经成了本科 QM 的标配教材，依我的经验来看读起来非常亲切易懂。- Schey 写的《Div, Grad, Curl, and all that》[1]。我不记得那本 QFT 书里涉及了多少向量微积分，但这本书可以说是彻底逆转了我本科的学习生涯。短短大概 120 页，就让我对 3D 微积分有了好得多的直观理解……
…book recommendations, the ones that come to the top of my mind are: - Griffiths' Quantum Mechanics [0]. It's become a pretty standard undergrad QM text, and in my experience was very approachable. - Div, Grad, Curl, and all that by Schehey [1]. I don't remember how much into vector calculus the QFT book got, but this one turned the tide of my undergrad personally. For ~120 pages it gave me a better intuition with 3D calculus…
……Shakarchi 的《Complex Analysis》（复分析），普林斯顿大学出版社，2003年。* 同样有用的还有：Bott 和 Tu 的《Differential Forms in Algebraic Topology》，Springer，1982年。尤其看看 1.1-1.3 节。* 还有：H. M. Schey 的《Div, Grad Curl and All That》，Norton，2005年。* 还有：Hubbard 和 Hubbard 的《Vector Calculus, Linear Algebra and Differential Forms》，Prentice Hall 1999年。* 还有：T. Needham 的《Visual Complex Analysis》（复分析可视化方法），牛津大学……
…Shakarchi, Complex Analysis , Princeton University Press, 2003. * Also useful: Bott and Tu, Differential Forms in Algebraic Topology , Springer, 1982. See especially 1.1-1.3. * Also useful: H. M. Schey, Div, Grad Curl and All That , Norton, 2005. * Also useful: Hubbard and Hubbard, Vector Calculus, Linear Algebra and Differential Forms, Prentice Hall 1999. * Also useful: T. Needham, Visual Complex Analysis , Oxford University…
我读本科和研究生学 EE 的时候，帮我搞定电磁学的不二“宝典”就是《Div, Grad, Curl, and all that》（http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161）。在我那个年代还是第 1 版，不是现在的第 4 版。我还看到另一本好评满满的书叫《A Student's Guide to Maxwell's…
When I was an undergrad and graduate EE student, the "go to" book to help with electromagnetics was Div, Grad, Curl, and all that (http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161). Back in my era it was the 1st edition of the book, not the 4th. I see another book with good recommendations, A Student's Guide to Maxwell's…
……如果你想“用死磕的方式学微积分”，可以去读 Apostol——比如你想以极其严密的方式学微积分、为继续深造打下扎实基础的话。而 Schey 写的《Div, Grad, Curl and all That》则是一本通俗、精炼的向量微积分小书。我个人没读过，但听过很多好评。要实现你眼前理解麦克斯韦方程组的目标，这大概是最快的一条路了。免费在线副本：ftp://collectivecomputers.org:21212/books/morebooks/Mathematics/Div,%20Grad,%20Curl%20and%20All%20That%20-%20Shey.pdf……
…Apostol if you want to "learn calculus the hard way" -- e.g. if you want to learn calculus in a rigorous manner that prepares you well to keep going. An informal, brief book on vector calculus is Schey's Div, Grad, Curl and all That. I have not read it personally, but I have heard good things about it. It is probably the quickest way of achieving your immediate goal of understanding Maxwell's equations. Free online copy: ftp://collectivecomputers.org:21212/books/morebooks/Mathematics/Div,%20Grad,%20Curl%20and%20All%20That%20-%20Shey.pdf…
关于这个主题还有一本书叫《Div, Grad, Curl and all that》https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161，如果是偏物理思维的人我强烈推荐，但如果是偏纯数学思维的人我一点都不推荐。
There's also a book on the subject called "Div, Grad, Curl and all that" https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161 which I would highly recommend to physics-minded folks, but would not recommend at all to maths-minded folks.