1st Edition

Vectors and Vector Operators



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ISBN 9780852745854
Published January 1, 1987 by CRC Press
64 Pages

USD $54.95

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Book Description

Vectors and Vector Operators provides an introduction to the use of vectors and vector operators that will be especially helpful to first-year undergraduates of the physical sciences. The vector forms of many of the equations of physics clearly demonstrate the essential geometrical relationships between the quantities involved. Topics covered include vector algebra, products of vectors, differentiation of vectors, the gradient operator, and the divergence and curl of vector fields. Throughout the text, the author emphasizes the application of vector techniques to problems in physics and includes many worked examples.

Table of Contents

VECTOR ALGEBRA
Description of vectors
Scaling, addition and subtraction of vectors
Decomposition and resolution of vectors
Examples of vector addition from physics

PRODUCTS OF VECTORS
The scalar product
The vector product
Products of three or more vectors

DIFFERENTIATION OF VECTORS
Definition of the derivative
Particle dynamics
Plane polar coordinates and circular motion

THE GRADIENT OPERATOR
Scalar and vector fields
Partial derivatives
The gradient operator
Examples of the gradient operator

THE DIVERGENCE OF A VECTOR FIELD
Line, surface and volume integrals
The meaning of the divergence of a vector field
Gauss's theorem
An equation of continuity
Some examples

THE CURL OF A VECTOR FIELD
Stokes's theorem
Interpretation of curl F
Double vector operators
Examples involving curl

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