# 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.

• Preface

Chapter 1. Vectors and Vector Addition

1.1 Vectors

1.2 Representation of Vectors

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

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

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
• Published: January 1, 1963
• Imprint: Pergamon
• eBook ISBN: 9781483141930