Geometrical Vectors (Chicago Lectures in Physics)

Rating:
Summary: Invaluable -- Div, Grad Curl ++
Review: 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".

Rating:
Summary: A Short, Fascinating Book. Buy This One.
Review: 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.

Rating:
Summary: A Short, Fascinating Book. Buy This One.
Review: 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.

Rating:
Summary: Incredibly great!
Review: I have never read such a book like this. I really hope that many Japanese universities will use the text.

Will I be able to read the next "Geometrical Tensors"?


Rating:
Summary: A Great Book too bad the tensor one never got here
Review: i have read very good books on vector analysis and i know how a
good book look like ...i am very sorry to all the reviewers
that calimed good about this book but it is not.
the idea and the approach are excellent but the implemantation
is terrible...sad.
here is why ..
1- there is no a single proof of any thing the author proposed,
ex: the dot product of a stack and arrow is the number of sheets
that spaned by the arrow...why it is so ?,,,no answer.
2-alot of text descriping operations without illustration makes
you read the paragraph many times and hope that you get what is
in the author's mind ...actually there are many illustartions in
the book but since the approach is intended to be geometrical
then this amount is very less than enough.
3-many things the author said its obvious or its clear and as a
matter of fact they do not seem so at all.
ex: joining the sheets of stack field together that result in loose edges ,the author said ..its clear that thses loose edges
will themselves constitute a sheaf field...sorry this is not clear why..again no proof.
4-the chapter on coordinates and componets is just a misery.
5-no examples at all of any chapter that we can see and compare
this is the traditional way to solve it and this is the geometrical way and then we can get the insight at laest,but no.
6-no solutions to any problem of the ones at the end of every chapter.
7- the style of writing is extremely boring and not clear at all.
the 2 stars i gave are for:
1- the concept of covariant and contravariant vectors is superiorly mastered by the idea of the stack vector and arrow vector...really nice.
2- the price is ok.
to advice any one to buy this book is difficult because this book is like a medicin "is bitter but it can cause cure",
in other ohnest words it is not an educational book in any sense.

Rating:
Summary: Mathematical Treat
Review: I was wrong, wrong, Wrong to fault the first set of equations in this book. These equations are CORRECT -- they are the true determinants of the 3x3 matrix represented by the cross products AXB=C and DelXF, as given in the text.

The remainder of the text, however, still remains with several errors. (For instance, the distance vector d goes from positive to negative, not as it is written "...from negative to positive...."

However, I am greatly relieved to be proven wrong about the equations. After all, I paid a lot of money for this book, and expect to see flawless analyses. If I have to end up correcting many parts of the book then who's teaching who, huh? I don't pay out good money just so I can end up teaching the teacher. Where's my salary, then, huh!

Rating:
Summary: new visual metaphors
Review: 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:
Summary: A great companion to math and physics
Review: 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:
Summary: A great companion to math and physics
Review: 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:
Summary: An enlightening text
Review: 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.