Concise Vector Analysis

Concise Vector Analysis

The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division

1st Edition - January 1, 1963

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  • Author: C. J. Eliezer
  • eBook ISBN: 9781483141930

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Description

Concise Vector Analysis is a five-chapter introductory account of the methods and techniques of vector analysis. These methods are indispensable tools in mathematics, physics, and engineering. The book is based on lectures given by the author in the University of Ceylon. The first two chapters deal with vector algebra. These chapters particularly present the addition, representation, and resolution of vectors. The next two chapters examine the various aspects and specificities of vector calculus. The last chapter looks into some standard applications of vector algebra and calculus. This book will prove useful to applied mathematicians, students, and researchers.

Table of Contents


  • Preface

    Chapter 1. Vectors and Vector Addition

    1.1 Vectors

    1.2 Representation of Vectors

    1.3 Vector Addition

    1.4 -a, O, λa

    1.5 Resolution of a Vector

    1.6 Point Dividing AB in the Ratio m:n

    1.7 Centroid or Mean Centre of n Points

    Exercises

    Chapter 2. Products of Vectors

    2.1 Scalar Product

    2.2 Vector Product

    2.3 Triple Products

    2.4 Mutual Moment of Two Lines

    2.5 Positive and Negative Triads

    Exercises

    Chapter 3. Vector Calculus

    3.1 Vector Function of a Scalar

    3.2 Unit Tangent Vector Τ

    3.3 Functions of a Vector

    3.4 Map of a Field

    3.5 Directional Derivative

    3.6 Gradient Vector

    Exercises

    Chapter 4. Vector Calculus

    4.1 Line Integrals

    4.2 Line Integral of Grad φ

    4.3 Surface Integrals

    4.4 Volume Integrals

    4.5 Divergence

    4.6 Gauss's Transformation

    4.7 Curl A

    4.8 Stokes' Theorem

    4.9 The Operator ▽

    4.10 The Laplacian Operator

    4.11 Orthogonal Curvilinear Coordinates

    Exercises

    Chapter 5. Some Applications

    5.1 Equivalence of Force Systems

    5.2 Poinsot's Central Axis

    5.3 Space-Curve

    5.4 Infinitesimal Rotations. Angular Velocity

    5.5 Angular Velocity of a Rigid Body

    5.6 Gauss's Theorem

    5.7 Gravitational Potential

    5.8 Equipotential Surfaces

    5.9 Green's Theorems

    Exercises

    Index

Product details

  • No. of pages: 164
  • Language: English
  • Copyright: © Pergamon 2013
  • Published: January 1, 1963
  • Imprint: Pergamon
  • eBook ISBN: 9781483141930

About the Author

C. J. Eliezer

About the Editors

W. J. Langford

E. A. Maxwell

I. N. Sneddon

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