Customer Reviews

Vector Calculus

5 star:		(6)
4 star:		(4)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

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.

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.

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.

This book is very clear, but is mostly a collection of work with very little explanation. This is good when you understand the concepts; there is less to lead you astray. However, if you don't grasp an idea from what is provided, there is little recourse. I used this book in conjunction with the (ubiquitous) Stewart multivariate calculus book. It's not very expensive so I reccomend it.

Very good introduction to Vector Calculus.Perfect appropriated for home study when you have a relative good knowledge of basic Calculus.
Theorems and formulas are physicaly supported in there explanation.Some proofs in the chapter of Tensors are less rigor to make them understandable.
Also contains some beautiful examples and exercises (could be more) of Mathematical Physics.Good balanced structure of the subject matter who brings you to the equation of Navier-Stokes and more in the last short chapter of applications.
Very readable book that I could understand entirly without help,even after leaving school with a limited mathematical education 25 years ago.

{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.

If there is one thing I adore about Springer books is that they are cheap, to the point, and very accessible. This book is no exception. I used this book for self study after I took a Calculus III course. My understanding of the concepts I learned in class improved two-fold. There is really nothing negative I can say about this book. It is probably the best buy I've ever made yet. I wish all college texts were like this.

I am using this book to review vector calculus and have found that this text gives much insight into the physical nature of vectors. As a practicing engineer, I like that it omits lengthy proofs and gets to the point quickly. My understanding of the subject has increased and been reinforced since first taking the vector calculus course in college. The conceptual framework behind div, grad, curl and associated theorems is well explained. I like the association between vectors and matrices to facilitate computations. Use this text for an applications-oriented book on the subject. If you are interested in more mathematical proof then this would not be the book. The author has answers to all problems making this a great self-study text in a minimum of time. After going through this book, the language of theoretical aerodynamics is much more understandable and has given me much insight into the subject.

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.

I bought this book based on the other good reviews here and I was solely dissapointed. I have a Degree in Physics and Engineering and a Masters in Engineering as well and I bought this book to brush up my rusty fundamentals in prepping for a new job that involves a heavy amount of Electromagnetics which naturally means going back and redoing my Vector Calculus. Mr.Mathew does not believe in delving deep into any subject. Note that this is a very thin book, the theme here is more a stating of the facts than a rigorous treatment that would delve into each building block of Vector Calculus. So, if you are looking for an in-depth approach, lots of solved problems then dont buy this book.