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25 of 26 people found the following review helpful:
5.0 out of 5 stars
Invaluable -- Div, Grad Curl ++, March 15, 2004
This review is from: Geometrical Vectors (Chicago Lectures in Physics) (Paperback)
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".
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20 of 20 people found the following review helpful:
5.0 out of 5 stars
Lucid, breathtaking, dazzling, November 23, 1998
By A Customer
This review is from: Geometrical Vectors (Chicago Lectures in Physics) (Paperback)
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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19 of 19 people found the following review helpful:
5.0 out of 5 stars
A great companion to math and physics, July 25, 2003
This review is from: Geometrical Vectors (Chicago Lectures in Physics) (Paperback)
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!
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