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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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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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