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Title: Geometrical Vectors (Chicago Lectures in Physics) by Gabriel Weinreich ISBN: 0-226-89048-1 Publisher: University of Chicago Press Pub. Date: May, 1998 Format: Paperback Volumes: 1 List Price(USD): $17.50 |
Average Customer Rating: 4.45 (11 reviews)
Rating: 5
Summary: A great companion to math and physics
Comment: 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!
Rating: 4
Summary: new visual metaphors
Comment: New visual metaphors for different kinds of vectors in 3-space: arrows, stacks, thumbtacks, and sheaves (corresponding to contravariant, covariant, and two forms of tensor). Visual and helpful proofs of Gauss's theorem, and Stoke's theorem, and div, grad and curl. I suspect the book would have been better had he included tensors explicitly. Very valuable for anyone doing vector analysis.
Rating: 5
Summary: A Great Book too bad the tensor one never got here
Comment: This book is one of the best books on vectors that I have ever read, and believe me I have read many. It was one of the easiest reads that I have ever encountered in a math book. Everything is explained very well but a very interested student will have to go somewhere else to find meaning to many of the vector types. I would have like to to see more detail on N dimensions or even four since that is what relativity requires. Overall though a great book and an extremely easy read.
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Title: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus by Harry M. Schey ISBN: 0393969975 Publisher: W.W. Norton & Company Pub. Date: August, 1997 List Price(USD): $17.95 |
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Pubns Pub. Date: 01 April, 1989 List Price(USD): $14.95 |
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Title: A History of Vector Analysis : The Evolution of the Idea of a Vectorial System by Michael J. Crowe ISBN: 0486679101 Publisher: Dover Pubns Pub. Date: 09 February, 1994 List Price(USD): $12.95 |
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Title: Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age by Paul J. Nahin ISBN: 0801869099 Publisher: Johns Hopkins Univ Pr Pub. Date: November, 2002 List Price(USD): $22.95 |
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Title: Schaum's Outline of Vector Analysis by Murray R. Spiegel ISBN: 007060228X Publisher: McGraw-Hill Trade Pub. Date: 01 June, 1968 List Price(USD): $16.95 |
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