Geometrical Vectors (Chicago Lectures in Physics) 1st Edition by Gabriel Weinreich (PDF)

Description

Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject.Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students’ prior knowledge and geometrical intuition.Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is deep! While lacking the formal rigor of vector analysis or exterior calculus this book attempts to remedy the lack of intuition that often accompanies such treatments (read the preface of the book).In this book the author sneaks in clifford algebra, forms and applications to physics, he gives us a method of calculation that opens up the vector calculus you already knew and gives a great way to ‘draw’ many phenomenon in physics.The author has an important agenda in this volume and that is to distinguish between objects that naturally behave differently. It has been the legacy of Gibbs and Heaviside for us to flounder in the 3-d application/misapplication of Hamiliton’s quaternions. The reader is led to realize that identifying everything with contravariant vectors (arrows) is wrong and damaging to our intuition of phenomenon.I highly recommend this book. It may seem hokey at first with odd names like thumbtack and swarm but it portrays deep mathematics in a beautiful manner. Work hard on it, apply it to physics and mathematics and be surprised at what you find! This sort of geometrical analysis is hard to find (try Gravitation by MTW or Applied Differential Geometry by Burke) at this level.Remember it is meant to be an affordable companion to courses on vector and tensor analysis, and what a companion it is!

⭐I have to admit, when I first started reading the book, I was ready to dismiss it all as nonsense…I mean really, vectors are arrows, not a stack or thumbtack or any of the other “flavors” of vectors that are introduced in the book. I kept reading, and eventually the light clicked on…maybe I’m slow. Or maybe I simply still bear the bruises from my high school physics teacher beating the whole “arrow: magnitude and direction” aspect of vectors into me.Weinreich discusses vectors, in their many forms (contravariant, covariant, etc), almost entirely divorced from anything to do with physical laws. Relying on our natural human intuition and perception capabilities, this book explores the definition and manipulation of vectors and vector fields as simple geometric objects existing in three dimensional space where rulers are forbidden. Along the way, we learn about the simplicity, power, and if I may dare say, the beauty, of the branch of mathematics known as vector analysis.This is a great book to accompany a course or a more traditional book on the topic (e.g.

⭐). I found the book to be easy to read and comprehend (and I am an engineer, not a physicist or mathematician). I think some of the figures could have used a little work, seeing how the whole book is based on geometry arguments.

⭐This book offers an unorthodox account of three dimensional vector calculus which uses a host of nonstandard terminology. But while a student of vector calculus is likely to find some of the material in this book initially very helpful, they will quickly outgrow it.The author has a list of the limitations of this work near the end. Among them: good only for three dimensions, limited to flat spaces, and limited to definite metrics. But even the student who expects their work to be limited to three dimensional Euclidean space will find the approach of this book limited by its lack of coverage of dyadics.A stepping stone on the way to tensor calculus, and definitely not suitable as an introduction to vector calculus.

⭐Excellent book, however Professor Weinreich gives no references. One wonders whether he was aware of the work of Grassman/Clifford/Hestenes/Dolan and Lasenby,…As much as I like this book, I think time devoted to Hestenes et.al. will lead to a broader perspective and more people to share it with.

⭐Very interesting stuff but there is little consideration, if any, on how to tie this rather unorthodox presentation with almost every and any other book in or out of print. In contrast, “Gravitation” by Misner-Thorne-Wheeler offers the same geometrical insights in a way that ties nicely with whatever else one is likely to read about tensors and differential forms (two concepts about which Weinreich is mysteriously silent). So if you own Misner-Thorne-Wheeler you do not need Weinreich, and if you don’t then you should, in which case you’ll avoid Weinreich and learn some relativity theory too. However, after you read Misner-Thorne-Wheeler you may want to check your understanding of some concepts by seeing if you can find their equivalents in Weinreich’s idiosyncratic treatment.

⭐Even when the product wasn’t damaged in shipping, it is still sub par printing and binding quality. I have initiated the return process, but eventually decided that I would receive the same crappy product back. Never mind, just don’t order there.

⭐This is Indian paperback reprint softcover edition. Not the original Chicago University Press USA edition.

⭐Snygg著”Clifford Algebra”に素晴らしい書評を書いていた人が強く薦めていたので、興味を持ち読んでみました。予想もしなかった内容で、他に類を見ない書物です。本書を手に取るまでは、「いまさらベクトルなんて」とも思ったのですが、これを読むと、私の浅学が良く分かりました。何となく霧がかかっていた部分も、晴れてくるような爽快感がありました。大学などでベクトル解析を勉強したものの、何となく腑に落ちない点が残っている人であれば、必ずや恩恵を受けられる筈です。内容は、ベクトルの内積、外積、grad、curl、div、など基本的なものですが、座標変換の元での不変性が内容を貫いており、それを武器に、従来のベクトル解析の教科書が如何におかしな内容かを示しています。ベクトル命名法も面白く、arrow、stack、thumbtack、sheaf、などが図解入りで登場します。これにより、反変、共変ベクトルや双対基底も理解できます。”Geometrical Tensors”も出ればよいのですが。

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