The Vector analysis problem solver
Covers all topics of vector calculus, including vector differentiation and integration, theorems of Green and Stokes, and the divergence theorem. Special topics in tensor notation, linear algebra, differentiation geometry, and curvilinear coordinates are also included.
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Chapter No Page
MAGNITUDE LINEAR DEPENDENCE
THE SCALAR PRODUCT AND THE VECTOR
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a x b apply b x c base vectors closed curve component conclude conservative conservative vector field Consider const coordinate system cube curl F defined definition denoted density determine direction divergence theorem domain dt dt dxdy dydx equal to zero Evaluate the integral expressed field F figure fluid force function f grad f gradient Green's theorem identity line integral linear combination linear transformation linearly independent magnitude normal vector Note obtain parametric equations partial derivatives particle path perpendicular position vector PROBLEM Prove radius real numbers region represents scalar field scalar function scalar product Show shown in Fig side of eq.(l solenoidal Solution sphere Substituting eq.(l surface integral three-dimensional unit normal vector unit vector vector field vector function vector product vector space volume integral written xy plane xy-plane