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Geometrical Vectors (Chicago Lectures in Physics (Paperback)) (Englisch) Taschenbuch – 6. Juli 1998

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Synopsis

This text introduces an approach for mastering the concepts of vectors and vector analysis 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 co-ordinates. It separates 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, this text provides a guide for any student of vector analysis. Clear line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.

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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.

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Von Ein Kunde am 23. November 1998
Format: Taschenbuch
I cannot sufficiently express my amazement at the geometry that is expressed in this book. The unification of seemingly bizarre sets of concepts into a geometrical "whole" is dazzling. The usefulness of this view to get a better motivation and feel for physics is a primary benefit, but the geometry that is presented here is satisfying in its own right. And, the exposition of the book is immpeccable, adding greatly to its beauty. This book is in a class with Feynman's "QED; The Strange Theory of Light and Matter" and Epstein's "Relativity Visualized". Buy it, as soon as possible...
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Format: Taschenbuch
I hardly need to add another Highly Recommended to the list of reviews. However, Professor Weinreich has assembled from his lectures an exceptionally interesting and intriguing geometrical approach to vectors. Not the conventional directed line segment approach, but one which questions which geometrical relationships are topologically invariant and which are not. This is not a difficult book, but I suspect that the more familiar the reader is with vector concepts, the more surprised and appreciative he will be.
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Format: Taschenbuch
Weinreich takes a somewhat unorthadox approach to the description the vector calculus in this text. His geometrical derivations, however, provide wonderful insight into the true significance of the divergence, gradient, and curl. Shey's text ("Div Grad Curl and All That") taught me to perform the calculations, but Weinreich taught me what those calculations mean.
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Until I looked at this and Schouten's book I didn't have a visual feel for the different types of vectors;unlike Schouten he is comprehensible to someone with a limited math background. I sure hope he does a sequel on tensors.
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Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: 4.4 von 5 Sternen 19 Rezensionen
27 von 27 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Lucid, breathtaking, dazzling 23. November 1998
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format: Taschenbuch
I cannot sufficiently express my amazement at the geometry that is expressed in this book. The unification of seemingly bizarre sets of concepts into a geometrical "whole" is dazzling. The usefulness of this view to get a better motivation and feel for physics is a primary benefit, but the geometry that is presented here is satisfying in its own right. And, the exposition of the book is immpeccable, adding greatly to its beauty. This book is in a class with Feynman's "QED; The Strange Theory of Light and Matter" and Epstein's "Relativity Visualized". Buy it, as soon as possible...
32 von 33 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Invaluable -- Div, Grad Curl ++ 15. März 2004
Von Ken Braithwaite - Veröffentlicht auf Amazon.com
Format: Taschenbuch
I actually have a few complaints about this book, but the core material is so helpful and instructive that they don't much matter.
This book explains vector and the beginnings of tensor analysis with new visual metaphors for vectors: lines, sheaves, thumbtacks, stacks. The dot and cross products can be visualized with these metaphors, and the various forms of Stokes/Gauss theorems proven visually.
This is great stuff for anyone going beyond the basics in vector analysis -- which would be anyone in pure math or physics, and some engineers.
You do need to use this as an adjuct to a conventional text or course.
This is the more sophisticated and general version of "Div, Grad, Curl and All That".
25 von 25 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen A great companion to math and physics 25. Juli 2003
Von Kevin Roberge - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
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!
23 von 24 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen An enlightening text 24. Dezember 1999
Von nkhanson@midway.uchicago.edu - Veröffentlicht auf Amazon.com
Format: Taschenbuch
Weinreich takes a somewhat unorthadox approach to the description the vector calculus in this text. His geometrical derivations, however, provide wonderful insight into the true significance of the divergence, gradient, and curl. Shey's text ("Div Grad Curl and All That") taught me to perform the calculations, but Weinreich taught me what those calculations mean.
27 von 29 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen A Short, Fascinating Book. Buy This One. 28. November 1999
Von Michael Wischmeyer - Veröffentlicht auf Amazon.com
Format: Taschenbuch
I hardly need to add another Highly Recommended to the list of reviews. However, Professor Weinreich has assembled from his lectures an exceptionally interesting and intriguing geometrical approach to vectors. Not the conventional directed line segment approach, but one which questions which geometrical relationships are topologically invariant and which are not. This is not a difficult book, but I suspect that the more familiar the reader is with vector concepts, the more surprised and appreciative he will be.
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