Introduction to Vector Analysis
Focusing on vector analysis, this book aims to meet the professional needs of the engineer or scientist, and to give the mathematician an understanding of the three-dimensional versions of the theorems of higher geometry. Concepts are described geometrically and then examined analytically, allowing the reader to visualize a concept before it is formally defined.
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VECTOR FUNCTIONS OF A SINGLE VARIABLE
SCALAR AND VECTOR FIELDS
LINE AND SURFACE INTEGRALS
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angle angular velocity arc length axes axis charge closed curve component of F compute conservative constant coordinate curve coordinate system curl F curvilinear coordinates cylindrical coordinates defined denote density differentiable directed line segment div F divergence theorem domain dt dt dx dy equals equations Example Exercise expression field F FIGURE Find flow lines flux formula geometrical given grad gradient Green's theorem Hence identity interpretation intersection isotimic surfaces Let F line integral line segment magnitude matrix nonzero normal component oriented origin orthogonal parallel parallelepiped parametric perpendicular point in space point x,y,z position vector potential proof quaternions radius rate of change region represented rotation scalar field Show simply connected Solution spherical coordinates surface integral tangent transformation triple scalar product unit vector vector analysis vector field vector product volume integral xy plane zero