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Vector Calculus

  • Textbook
  • © 1998

Overview

Authors:
  1. Paul C. Matthews

    1. School of Mathematical Sciences, University of Nottingham, University Park, UK

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  • Paul Matthews is a young writer with an excellent research record and teaching experience at both MIT and Nottingham - Up to date and of relevance to today's students - Full use is made of the elegant and concise suffix notation
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-ix
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  2. Vector Algebra

    • Paul C. Matthews
    Pages 1-20

  3. Line, Surface and Volume Integrals

    • Paul C. Matthews
    Pages 21-43

  4. Gradient, Divergence and Curl

    • Paul C. Matthews
    Pages 45-64

  5. Suffix Notation and its Applications

    • Paul C. Matthews
    Pages 65-82

  6. Integral Theorems

    • Paul C. Matthews
    Pages 83-98

  7. Curvilinear Coordinates

    • Paul C. Matthews
    Pages 99-113

  8. Cartesian Tensors

    • Paul C. Matthews
    Pages 115-130

  9. Applications of Vector Calculus

    • Paul C. Matthews
    Pages 131-152

  10. Back Matter

    Pages 153-182
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Keywords

About this book

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.

Reviews

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

 

Authors and Affiliations

  • School of Mathematical Sciences, University of Nottingham, University Park, UK

    Paul C. Matthews

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