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Geometrical Vectors (Chicago Lectures in Physics), by Gabriel Weinreich
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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.
- Sales Rank: #888731 in Books
- Published on: 1998-07-06
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .40" w x 6.00" l, .45 pounds
- Binding: Paperback
- 126 pages
From the Back Cover
Physics/Mathematics
Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most textbooks cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject.
By contrast, 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 a set of problems is provided at the end of each chapter (except the Epilogue) to deepen understanding of the material presented. Pertinent physical examples are cited to show how geometrically informed methods of vector analysis may be applied to situations of special interest to physicists.
Most helpful customer reviews
8 of 8 people found the following review helpful.
Very lucid
By Lance C. Hibbeler
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. Gravitation). 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.
25 of 25 people found the following review helpful.
A great companion to math and physics
By Kevin Roberge
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!
6 of 9 people found the following review helpful.
Mathematical Treat
By A Customer
A fresh look at what can be a dusty subject, demonstrates simple yet powerful unifying concepts. This book is a treat.
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