Vector Calculus [Paperback]

Paul C. Matthews (Author)

Book Description

Publication Date: June 12, 2000 | ISBN-10: 3540761802 | ISBN-13: 978-3540761808 | Edition: Corrected

Vector calculus is the foundation stone on which a vast amount of applied mathematics is based. Topics such as fluid dynamics, solid mechanics and electromagnetism depend heavily on the calculus of vector quantities in three dimensions. This book covers the material in a comprehensive but concise manner, combining mathematical rigour with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which is essential for a full understanding of the subject. Each chapter concludes with a summary of the most important points, and there are worked examples that cover all of the material. The final chapter introduces some of the most important applications of vector calculus, including mechanics and electromagnetism.

Editorial Reviews

Review

P.C. Matthews Vector Calculus "Written for undergraduate students in mathematics, the book covers the material in a comprehensive but concise manner, combining mathematical rigor with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which essential for a full understanding of the subject." — ZENTRALBLATT MATH  

Product Details

• Paperback: 200 pages
• Publisher: Springer; Corrected edition (June 12, 2000)
• Language: English
• ISBN-10: 3540761802
• ISBN-13: 978-3540761808
• Product Dimensions: 9.6 x 6.8 x 0.5 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #275,369 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

50 of 52 people found the following review helpful:

5.0 out of 5 stars Excellent for self-study, January 1, 2002

By 

Doug201 (New York City, NY) - See all my reviews

This review is from: Vector Calculus (Paperback)

I purchased this book to further my self-study of Physics. Simply put, this is the best written book I have read on any math subject (although Spivak's Calculus is also very good, but is on a different topic).

A wonderful feature of this book is the problems - and complete solutions - provided throughout. The problems are not so extensive that you will skip them (there about 10-20 per chapter, as opposed to many other texts which have fifty or more) nor so difficult that you will give up in frustration. Indeed, for self study, the simple fact that there are answers is key; the fact that they are not of the sort where you are asked to derive new math or otherwise are treated as if you are a "student who believes he is to become the next Einstein" is a refreshing change.

This book covers vectors (of course), various vector integrals (line, surface, and volume integrals), and gradient, divergence and curl (if you ever wondered what that odd upside down triangle symbol is, you will learn), before moving into more advanced topics. It briefly covers "suffix notation" and tensors, as well as transformations into different coordinate systems. In sum, about half the book is wonderful and immediately useful, and the other half will become more useful as I encounter it in the course of learning physics.

That said, I wish it went into more detail in the "suffix notation" section, which is quite confusing (although several readings helps) as well as more on tensors, which extensively employs the suffix notation.

I have been told, without confirmation, that Springer is known for it's clarity; this book certainly is extremely clear, well written, and has allowed me to finally begin to understand many parts of mathematical physics which were previously Greek to me.

23 of 23 people found the following review helpful:

5.0 out of 5 stars not 80% but..., August 16, 2002

By 

"itsux" (Korea) - See all my reviews

This review is from: Vector Calculus (Paperback)

Someone has said in a review that
Its mathmathical rigor is about 80%
but as a student majoring in math I
cannot agree with that. I can't give
it more than 60%.
It's the kind of the book which will
never be met in the math class.
but that does not mean this book is not
good.

it lacks in mathmatical rigor but that's
not problem. it's quite clearly written,
easy to read, and most of all It explains
you the 'meaning' of the equation.
lots of math book you should try youself
very hard to understand its meaning.
they give you the proofs of theorems
definitions of mathmatical objects
but not the meaning nor its context.
that's something you should find out.

but this book gives you that. It explains
you what is the meaning of it.

If you are majoring in math. this can be
a gread secondary text. If you are not.
then this should be your first choice.

22 of 25 people found the following review helpful:

3.0 out of 5 stars nice read, no rigor, too few exercises, September 20, 2004

By 

Jacob Sznajdman (Gothenburg, Sweden) - See all my reviews

This review is from: Vector Calculus (Paperback)

This book is quite easy to read, and it gives a good intuitive picture of the subject. Mathematicly it is not of so much value. I think its very good for someone who wants to study electromagnetic fields, or some other fields in physics and want to be able to calculate different integrals (perhaps there are more applications than physics).

Physicists often do non-rigorous arguments, and it is very possible to do so and still be certain what you are doing makes sence. Rigor can take up too much of your time :)

But if you want to go deep into physics I would recommend spending your money on some deeper and more rigourous text, it will be useful in the long run.

There are some incorrect proofs, that I believe are absolute nonsense, but as i said, this book is only good for your feeling of vector calculus and ability to calculate integrals.

I would give the book a 4/5 but you simply cant learn calculation without many problems of varying difficulty. If this is your only book, it is absolutely essential that you get some kind of collection of exercises too. There are only 9 exercises on the chapter on curvilinear coordinates (cylindrical, spherical, etc.)

I think you can get a better book for the money, but its not too bad.