Introduction to Vector AnalysisFocusing 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. |
Contents
VECTOR ALGEBRA | 1 |
Tensor Notation | 51 |
VECTOR FUNCTIONS OF A SINGLE VARIABLE | 58 |
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Common terms and phrases
angle arc length axis closed curve component of F compute conservative constant coordinate system curl F defined denote df/ds differentiable directed line segment div F divergence theorem domain dt dt dx dy dz equal equations Example Exercise expression F₁ F₂ field F FIGURE Find flow lines fluid flux formula function Gauss's law given grad ƒ gradient Green's theorem Hence identity isotimic surfaces Let F line integral magnitude matrix nonzero normal component notation oriented orthogonal parallel parametric particle perpendicular point in space point x,y,z position vector potential proof quaternions radius region rotation scalar field scalar product Show simply connected smooth arc Solution surface integral tangent tangential component triple scalar product unit normal unit vector vector field volume integral xo,yo,zo xy plane zero ди дф дх ду