No calculus needed, but this is not an elementary book. Introduces vectors, algebraic notation and basic ideas, vector algebra and scalars. Covers areas of parallelograms, triple products, moments, angular velocity, areas and vectorial addition, and more. Concludes with discussion of tensors. Includes 386 exercises.
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Most Helpful Customer Reviews
17 of 18 people found the following review helpful:
5.0 out of 5 stars
everything you ever wanted to know about vectors,
By
This review is from: About Vectors (Dover Books on Mathematics) (Paperback)
About Vectors begins by setting forth the goal of defining vectors. The author then shows that there are problems with any definition of vectors. For example when are two vectors equal? When they have the same magnitude and direction, but what if one of those vectors is a free vector and the other a bound vector? After raising questions about what constitutes a vector the author goes through vector algebra. He is very thorough. The book cumulates in an introduction to quaternions and tensors. Throughout the book the author raises questions similar to the one above. I found this book very useful for learning both the algebra of vectors and also the ideas behind them. I highly recommend this book for anyone who needs to learn about vector algebra.
5 of 6 people found the following review helpful:
5.0 out of 5 stars
Excellent companion to linear algebra / physics courses,
By Jesse Taylor (North Idaho) - See all my reviews
This review is from: About Vectors (Paperback)
This is an excellent little book on vectors. It solidified my intuitive understanding of vectors and sharpened my mathematical thought processes in general.
I thought I knew plenty about vectors after going through linear algebra and calculus, but this book helped me discover and fill in many gaps in my understanding. Anyone could benefit from reading this -- however much they think they already know ... Plus it was just written in such a way that it was actually fun to read ... the way a good mathematics text should be! Very highly recommended.
2 of 2 people found the following review helpful:
3.0 out of 5 stars
Mostly elementary,
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Amazon Verified Purchase(What's this?)
This review is from: About Vectors (Dover Books on Mathematics) (Paperback)
Overall, I have to say this is a very well written book. It covers an important topic with very good explanation. However, I don't think it performs a necessary function. I bought this book as a 4th-year engineering student with years of experience with vectors from math, science, and engineering classes. What I found is that this book is a) far too elementary to be useful to anyone with significant experience with vectors, and b) too technical to be useful to anyone with no experience with vectors. Think of an experienced artist reading a book on the use of a paintbrush.
It is quite unlikely that a high school math or science teacher would use this book to explain vectors to students. Although the author's explanations are thorough and simple, the notation is too technical for that level. However, if you, like me, thought to buy this book expecting to deepen your understanding of the mathematics of vectors, you will probably be disappointed. This is a nearly complete list of topics of the first 5 of 6 chapters: Definition of vectors, parallelogram law, basic vector algebra (+, -, =), scalar (dot) product, vector (cross) product, and a number of applications of vectors (kinematics, forces & moments, angular motion, etc...) He also introduces tensors in the last chapter, but, in the author's own words: "This being a book about vectors, we have presented only the sketchiest account of tensors ..." If you want a book on vectors for completeness of a personal library, this is a good one to have. But if you just want the information, you probably know 90%+ of what's in this book if you're the kind of person that reads Dover math books or comes from science/engineering.
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