Free PDF Vector Analysis Versus Vector Calculus (Universitext)
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Vector Analysis Versus Vector Calculus (Universitext)
Free PDF Vector Analysis Versus Vector Calculus (Universitext)
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From the Back Cover
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Several practical methods and many solved exercises are provided. This book tries to show that vector analysis and vector calculus are not always at odds with one another.  Key topics include:-vectors and vector fields;-line integrals;-regular k-surfaces;-flux of a vector field;-orientation of a surface;-differential forms;-Stokes' theorem;-divergence theorem. This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.
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About the Author
Antonio Galbis and Manuel Maestre are currently professors of mathematics at the University of Valencia in Spain.
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Product details
Series: Universitext
Paperback: 392 pages
Publisher: Springer; 2012 edition (March 26, 2012)
Language: English
ISBN-10: 9781461421993
ISBN-13: 978-1461421993
ASIN: 1461421993
Product Dimensions:
6.1 x 0.9 x 9.2 inches
Shipping Weight: 1.5 pounds (View shipping rates and policies)
Average Customer Review:
4.3 out of 5 stars
4 customer reviews
Amazon Best Sellers Rank:
#323,231 in Books (See Top 100 in Books)
I wish there were separate ratings for the intellectual content of a book and its physical form. In the case of this particular text, I would give the content a rating of 5 (or more) stars while the binding and paper a 1 or 2 at most. To get the negative stuff out of the way, the quality of the paper and binding is poor. The paper feels cheap and stiff; the book itself looks warped; the binding is "segemented", for lack of a better word. In summary, I would go so far as to say that the production quality of a typical inexpensive Dover publication is far superior to this text. This, unfortunately, is the latest example of a long list of problems that I and others have had with Springer publications whose production is shoddy. I emailed their customer service department about this issue but received no response. Apparently, these problems don't concern them.With regard to the content, I really like what the authors have done. This text effectively fills the gap that currently exists between typical non-rigorous "vector calculus" texts that attempt to convey qualitative notions of the Stokes' theorem with physical and intuitive arguments and the most sophisticated treatments in the contexts of manifolds that would finds in texts such as John Lee's Introduction to Smooth Manifolds. The text by Galbis and Maestre is completely rigorous but the work is done exclusively in the context of submanifolds of Euclidean n-space. Consequently, the presentation is very concrete and hands-on.Mathematical sophistication is presumed in the sense that they assume the reader is comfortable with rigorous analysis of both one and several variables and basic linear algebra. Some of the things they state without proof for instance include the chain rule for multivariable functions, the Heine-Borel theorem and the uniform continuity theorem for continuous mappings defined on compact Euclidean spaces. The text should be pretty easy to read for people with this background.The authors make a very valid point that the notation and terminology surrounding this subject is not consistent in that different authors may define the same terms with slightly different meanings. In basic analysis everyone agrees on what it means for a set to be compact, connected and so forth, but there are many different ways that, say, a "regular curve" can been defined. What I particularly like about this text is that the authors are careful to note with precise references where other authors have defined a term to have a slightly (or completely) different meaning.So, in summary, I really like the content of this text and the way the authors have approached it. I thoroughly dislike the binding and fail to understand why such a text with such high-quality content must be subjected to such a low-quality production process.
What a spectacular book! If you love mathematics, as I do - buy this book; you will thank yourself for years!
If you want to understand the deep theory under Stokes' theorem...¡THIS is the book!!!
The text covers some key topics on intermediate-upper mathematics that can be very useful for students of mathematics at this level, but also (as it is my case)for physicists and computer scientists who, for one or another reason, wish to use the concepts explained and need to understand not only a set of equations butalso their geometric interpretation. The book, indeed, is illustrated with nice and enlightling B/W and color figures that add to it a great value. I am interested in this book because of the connection between differential geometry descriptions of surfaces and some algorithms to perform volume and surfaceregistration in 3D, a hot topic in medical image analysis, and I must say that it has clarified most of my doubts and has served me to refresh old concepts in anew way, much clear than when I studied them. I coincide with the previous reviewer in the low quality of the binding, as long as too small margins in the pages, and this is the only reason for not giving thebook the five-star grade that the content would deserve, but I suppose that Springer wants to keep the costs low, specially in the current times. Summarizing, a higly recommendable text for people that need this knowledge explained in a clear and, as much as possible, intuitive way without sacrificingmathematical rigor and soundness.
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