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Vector Analysis Problem Solver (Problem Solvers Solution Guides), by The Editors of REA, Emil G. Milewski Ph.D. Chief Editor
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Covers all topics of vector calculus, including vector differentiation and integration, theorems of Green and Stokes, and the divergence theorem. Special topics in tensor notation, linear algebra, differentiation geometry, and curvilinear coordinates are also included.
- Sales Rank: #1348609 in Books
- Published on: 1985-01-17
- Released on: 1985-01-17
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Dimensions: 2.19" h x 6.70" w x 9.99" l,
- Binding: Paperback
- 1272 pages
Most helpful customer reviews
27 of 35 people found the following review helpful.
They worked hard at it, but it's unacceptable
By Stan Vernooy
This book apparently has two primary goals: to cover a large amount of material and to do so at as low a price as possible. Those two goals are astonishingly well achieved, but the deficiencies are so severe that they render the book unacceptable.
First, the printing is substandard: unadorned Courier or something similar, not right-justified, and is so primitive that the publishers cannot use much of the usual notation. Since vector analysis uses mathematical symbolism heavily, this is a major disadvantage. The same on-the-cheap approach applies to the diagrams. There is no color, and the diagrams are composed almost entirely of compass-and-ruler constructions and notation in the same typeface as the text.
Second, the index is inadequate. This book is likely to be used as a reference rather than read sequentially, so the index is important. This index doesn?t include some of the most fundamental terms or topics, such as "component" or "dimension". There are scores (if not hundreds) of references to derivatives in the book, and yet the index includes only five references to derivatives.
There is not a single reader exercise in the book (unless I missed something). The book is intended to be a demonstration of how Vector Analysis is done, so all the problems are worked out by the authors. If the readers have their own textbooks, this is not necessarily a big disadvantage. But this book, in the introduction, actually criticizes other texts for requiring the students to do exercises, and goes on to make the following stunning statement: "The staff of REA considers vector analysis a subject that is best learned by allowing students to view the methods of analysis and solution techniques themselves."
I can't overemphasize what an incredible statement that is. There are not two schools of thought on this issue. The idea that a student can learn Vector Analysis (or any mathematical topic) by watching someone else do it, makes as much sense as recommending that someone learn to play the guitar by listening to Eric Clapton. That one point of educational philosophy alone demonstrates conclusively that the book is incompetent.
The Problem Solver series is apparently produced with another eccentric belief, and one that is annoying for anyone accustomed to reading traditional math books. The publishers apparently believe (according to their own words in the introduction) that one of the shortcomings of other books is that they present material without first explicitly stating what the goal of each paragraph or section is. (In my experience, this criticism is sometimes valid, but usually not.) Their solution to this is to make every word in the text, part of the statement or solution to a "Problem". However, these are not problems in the usual sense. For example, the second "problem" in the book asks for the dimensions of five vectors which are presented in component form. At that point in the book (page 3), the word "component" has not been defined, no vectors have yet been presented in component form, and the equality between dimension and the number of components has not yet been mentioned. So this is not a "problem" that anyone would be able to solve if his knowledge were limited to what has been presented in the book up to that point. The book usually presents those necessary definitions in the course of "solving" the problem (although in this case, they don't define the word component, and as far as I can see they NEVER define that word. As I mentioned earlier, "component" and "dimension" are both missing from the index.) This entire quirky approach reminds me of that TV game where the contestants are required to respond with a question instead of an answer. It requires a pointlessly awkward presentation just to cram the material into their ideological system. The definitions and formulas are not designated separately, as in other books, but imbedded in the problem "solutions".
Most important, the book is full of mathematical errors. Page 22 refers to "vectors of the same magnitude" when they mean "vectors of the same dimension". Page 23 has a problem involving vector addition and subtraction, in which they present a1, b1, c1, a2, b2, and c2 as components of vectors (using subscripts), and proceed to use a1c1 as the DIFFERENCE between those two components (or the distance between the terminal points of the horizontal projections of vectors a and c, which is the same thing). Of course, they should have used c1 - a1. This is not just non-standard notation; it is simply mathematically wrong. And I believe they repeat that same error in other problems later on.
In proving an important theorem (the equivalence of the algebraic and geometric/trigonometric definitions of dot products), they suddenly pull out a formula from analytic geometry that very few calculus students in the US will ever have seen. Since the use of that formula renders the rest of the proof entirely trivial, the student will learn nothing at all about how to prove theorems from reading that proof. The same sort of thing happens in Problem 3-6, where they use a formula for finding the components of a projection - a formula which has never been mentioned before, and which they neither derive nor explain.
The book constantly rounds off intermediate results. This should never be done in these days of 12-digit calculators, and ESPECIALLY when the calculated number is to be used as input into an inverse trigonometric or exponential function. In fact, they don't even really round those numbers off - they just truncate them! This causes their final answers to be wrong in many cases, such as in Problem 3-11, where the answer should be the vector (0.279, 0.885, -0.373). This is amateurish. If the authors don't know better than that then they shouldn't be writing math books.
After reading "Problem" 3-16 on pages 81-82, I finally gave up entirely on this book. The problem statement asks for the cross product of two vectors, while sort of half-defining the cross product within the problem statement itself. Then, in the "solution", they don't find the cross-product at all! They find only the magnitude! They simply forgot to finish the problem!
This book was never competently proofread, peer-reviewed, or edited. Presumably that would have been too expensive. But this amateurish production is unusable for learning Vector Calculus. Not recommended.
3 of 3 people found the following review helpful.
An Indispensable Reference
By Herbert L Calhoun
Advance mathematical concepts (such as the idea of a "basis vector," for instance) cannot be fully grasped without eventually working through a "sample vector space" in which one devises his own basis vectors for the vector space in question. Once the idea is made real, through examples, the reader can then move on with confidence to the next concept.
This is of course the real value of the book, it helps build up confidence in "seeing how" both easy and more difficult problem are worked through. It gives example after example of actual problems for, not just "basis vectors," but also for a whole host of other difficult concepts in vector analysis and vector calculus.
A prudent reader would do well to take out his pencil and work through the examples in the book and then try one of his own devising. That is what I did and now I feel fairly confident that I again really understand these concepts.
One word of warning, the book assumes full understanding of all the concepts of vector analysis through linear algebra and vector calculus. For those like myself (who have not seen these concepts since grad school), it does not hurt to have a reference or two in each of these areas handy while working through the problems. I found the Marsden-Tromba book on vector calculus and the two-volume set by Jacobson on Linear Algebra to be quite sufficient to lean on for the needed theory prepping.
The only criticism I have of the book is that the flow of difficulty of the problems is a bit uneven. In most sections the flow is from "too simple" to "much too difficult" with nothing in between, which is yet another reason to have the text books handy to lean on. Most text books pose "immediate level" problems as exercises at the end of each chapter which can be used to fill in the blank between the easy and difficult problems solved in this book. Altogether, it is an indispensable reference book. Four stars
2 of 2 people found the following review helpful.
Great book.
By J. Alvarado
If you have taken a calculus based physics course and need some help going over some of the mathematics this book and the other rea books are great. If you have taken physics than you understand there is a lot of different notation so this book will be any easy read you. The way this book should be used is as an aid, since you are assumed to know calculus and some linear algebra you can just look up the problem you are working on and check your work with similar problems in the book. You should not use this book to learn from there is no such book that you can do that with, there has never been a book that covers a whole subject especially without a typo ever. This book is 25 years old and was discontinued since most american dont do this type of mathematics so there was no need for revisions. If you are coming from a physics background then this has more than enough steps for all its problems, if you are from a poor mathematics background then you will have problems and give up on the book. If you do have problems with mathematics the other rea books cover the material you need for the book( ie:calculus, Linear algebra, pre-calculus, algebra) well so that you can come back and read this book with ease.
Remember its a GUIDE and worth the price if you do physics and upper level mathematics. If you dont math/physics and you want a book that does everything then you can read the other reviews/complains.
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