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
Line Surface and Volume Integrals
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A X B angle angular velocity arc length axis component of F compute constant coordinate curves coordinate system curl F curvilinear coordinates cylindrical coordinates defined denote density differentiable directed line segment div F divergence theorem domain dt dt dx dy dz equals equation example exercise expression field F figure Find flow lines fluid flux force formula function geometrical given grad gradient Green formula Green's theorem Hence identity interpretation intersection irrotational field laplacian Let F line integral magnitude matrix nonzero normal component notation oriented origin orthogonal parallel parametric particle perpendicular position vector proof quaternions radius region right-handed rotation scalar field Show simply connected Solution sphere surface integral tangent tensor transformation triple scalar product unit vector V X F V X G vector analysis vector field vector potential vector product Verify volume integral xy plane zero