Vector Calculus

by Paul C. Matthews

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.

Genres: Mathematics, Textbooks, Physics, Science, Calculus

200 pages, Paperback

First published January 14, 2000

Reviews

[Rich Bergmann · Rating 5 out of 5]

This is the most approachable treatment of the subject (tensors) that I have read -- and I have read many books on the subject. To that add the author's excellent treatment of vector calculus and curvilinear coorodinates and the result is a book that is *always* with me as I study physics. No physics undergraduate should be without this book!

[Tianxing Weng · Rating 4 out of 5]

this book is pretty much just an introductory, I like how it is not so mathematically rigorous which makes it easier to give a rough impression about vector analysis. The last chapter which specifically deals with the application of what we've learned in the whole book, is absolutely a highlight of this little book. Finally, it is a textbook with solutions of its exercises! Although the exercises are not hard enough to make people totally understand the content, they are enough for people to get used to the language of vectors and tensors, and get prepared for a more rigourous intuition.

p.s. I like how it derives Navier-Stokes' equation from isotropic elastic solid.

[Salvador Достоевский · Rating 5 out of 5]

Read this book before studying electromagnetism and analytical classical mechanics.
Goes from elementary vector algebra to tensors and applications
Straight to the point, easy to follow, enough exercises (with solutions) and worked examples.
All theorems are proved, which is cool for the curious one.
Definitely recommend.

[Samir Rawas Sarayji · Rating 5 out of 5]

Excellent intro from first principles. Uses formal proofs at an accessible level (first year undergrad) and useful examples.

[Loki · Rating 4 out of 5]

Maybe the first time I've completed a textbook in full, and this is now some years after graduating... it was a brilliant refresher and I now feel confident to move on to more challenging stuff.