Item description for Vector Calculus by P. C. Matthews...
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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Est. Packaging Dimensions: Length: 0.5" Width: 6.5" Height: 9.25" Weight: 0.75 lbs.
Release Date Jun 12, 2000
ISBN 3540761802 ISBN13 9783540761808
Reviews - What do customers think about Vector Calculus?
Handicapped by a Big Slosh of English Snootiness and Geometrical Pomposity, but Jan 30, 2008
its selection of problems and its focus on vector calculus are both quite good. Perhaps both are excellent, but my current experience and intuition in this subject area prevent me from being more certain.
Either way, a much more physically intuitive approach with more problem-solution examples and less geometrical rigor is possible, that much is certain.
Most importantly, in-text solutions are provided. There is no problem with merely an answer, all have something more. There are way fewer problems as compared to a schaum's outline (on the order of 30 times fewer). Though it also costs two or three times more than a Schaum's, it's certainly much more physically intuitive than the Schaum's on vector/tensor analysis by Murray R. Spiegel.
I think this book would make its publisher and author a lot more money (by selling a hell of a lot more of them) if it were reduced in price. It would be a win-win for everybody who, I'm pretty certain, matters here.
Great intro for beginning undergraduate students Oct 17, 2007
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.
Well written & applications oriented Jan 18, 2007
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.
nice read, no rigor, too few exercises Sep 20, 2004
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.
Nice and Succinct Book on the Subject Jun 16, 2004
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.