Vectors and Vector Operators

Abstract

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