Vector Calculus

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{excuse me if my review does not flow. I'm not very good at connecting paragraphs. But I'll try to pinpoints things about these books. Hopefully you'll benefit from those.}

Like most other Springer books published under SUMS (Springer Undergraduate Mathematics Series) category, it shows following traits:

1) it follows a down to earth approach.
2) it is brief (if you cut out table of content, preface, index etc, you have 179 pages of reading material).
3) there are worked out examples in pretty much all sections.
4) exercises are at the end of each chapter. Worked out and fairly detailed solutions are at the end of the book.


Like other reviewers have mentioned, this book does not contain much of proof. Instead, explanations are given to justify a formula or how a formula can be thought of.

Another thing worth mentioning is the usage of Physics in this book. Author does make use of Physical examples sometimes, for example in section 1.2.1, Matthews uses F.d (force dot displacement) to illustrate application of dot product. These stuff are elementary Physics though. The more deeper usage of Physics is seen is at the end of the book. Last section of Chapter 7 provides two physical examples of tensor, namely Ohm's law and inertia tensor. Finally, the last chapter is all about Application of Vector Calculus which again involves Physics.


This book does NOT require you to know about vectors before hand. Infact, chapter one is all about vectors and it's properties (addition, dot product, cross etc). Even if you already know about vectors, it won't hurt to take a brief glimpse at this chapter.

This book should NOT be used as your only source for Vector Calculus course. I've heard some people say they've used this book as a text for Multivariable Calculus course, if you're in similar course, please get an additional text for yourself. I used Jon Rogawski's Calculus...quite of a decent book imo. A lot of other people recommend Stewart (i haven't used this one personally but i hear it's good). The issue is this book just does not have enough exercises for you. Plus, there is a whole lot more stuff covered in typical Multivariable text but is absent on this one (arc length, curvature, center of mass, tangent planes, directional derivatives, optimization and Lagrange multipliers to name a few). On contrary, the book covers Suffix Notation, Curvilinear coordinates, Cartesian Tensor, and Physical Applications which typically are absent in Multivariable text.


chapter on Suffix Notation is quite a good one actually. I was taking "Mathematical Methods for Physicist" course where our professor quickly went over Kronecker delta and alternating tensor and kept using it for quite some time. I had to look into this book to understand what they meant and how they can facilitate calculation involving gradient.

Vector Calculus Features

• ISBN13: 9783540761808
• Condition: NEW
• Notes: Brand New from Publisher. No Remainder Mark.
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Vector Calculus Overviews

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.

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Customer Review

Excellent Resource - Fleezle - Ann Arbor, Michigan United States
I think this is a terrific review of vector calculus for those in the sciences. It is clear, concise, and very readable. In fact I read it in just a couple days trying to brush up on my vector calculus for the start of a new job.

I don't think it would be a sufficient introductory resource, especially for someone without the relevant science background as most the examples would be meaningless. I also don't think this would be great for a mathematician as I feel it's depth might not be sufficient. But it was perfect for me and I feel like I now understand the governing fluid and heat transfer equations with more clarity than ever before.

Only thing I think was left out is the convective operator...

Also, I haven't read the Schey book, which seems to be popular, so I can't compare but I can't imagine it being better.

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