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Vector Calculus (Springer Undergraduate Mathematics Series) [Kindle Edition]

Paul C. Matthews
4.9 out of 5 stars  See all reviews (8 customer reviews)

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Book Description

Vector calculus is the fundamental language of mathematical physics. It pro­ vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top­ ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro­ gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un­ derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.

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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

 


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Most Helpful Customer Reviews
1 of 1 people found the following review helpful
4.0 out of 5 stars Very Good 20 Sept. 2011
By Matt M
Format:Paperback
Another reviewer on here says pretty much all I want to say. But I would like to emphasis the point that this book does require more than elementary vector arithmetic and such before you can grasp it really. I used this in the second year of my degree and had a good knowlegde of vectors and single variable calculus under my belt. I was laos familiar with aspects of multivariable calculus.

That said, this book was great in developing on that. It concisely delivers information well enough to ensure a graduate level understanding of all sorts of physics/engineering topics. It does pay special attention to integral theorems, grad div and curl and has a very useful section on suffix notation. This all paves the way for the penultimate chapter on Cartesian tensors. I did find it hard going at times, but if you are looking for a book that gives you a good grounding ready for application to a physical science, this is a good one.
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5.0 out of 5 stars Great intro for beginning undergraduate students 10 July 2013
Format:Paperback
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.
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5.0 out of 5 stars Very helpful 12 April 2015
Format:Paperback|Verified Purchase
A good book on Vector Calculus. All the key topics were clearly explained and demonstrated with plenty of exercises. It also explains the use of tensors as well as a way of calculating volume components which is much easier than finding the determinant of the Jacobian
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4 of 6 people found the following review helpful
Format:Paperback|Verified Purchase
I understand why the other reviewer has 0 positive feedback!

If you have never seen any vector calculus before I doubt you'll make it to chapter 4. And if you do, that is as far as you'll go for a few months!

However, this book is very short for what it covers. So you can move fast. It fast but concisely transitions from basic operations with vectors to the main theorems and concepts of vector calculus like Green's theorem, Line integrals etc. Then it has an introduction to tensors and finally covers some good applications of these operations and theorems.

I assume that for somebody that wants to rapidly move from basic vector operations to advanced concepts in vector calculus this is a good book and, if completely and patiently followed, it allows the reader to understand the subject to a level good enough for any undergraduate course that I can think of. Having said that, as I say above, I dont believe somebody with just some basic understanding of the algebra of vectors can finish this book without going nuts. Thus I recommend that, if you havent done that already, read some elementary vector calculus, geometry (with vectors) and basic differential equations before you read this. Basically, that the author assumes no previous knowledge is "partially correct" but doesnt necessarily mean that it will be the best book for such a person. This is indeed the case for many books like this one.

Overall, I found it very good, concise and stright to the point giving good definitions and explaining the important bits of vector calculus necessary to follow any course in electromagnetism, elasticity theory and the like.
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