 The Operator ∇ and Its UsesB. Hague Chapter 4 in An Introduction to Vector Analysis For Physicists and Engineers, 1970, pp 41-69 from Springer Abstract: Abstract The differential operator ∇ was introduced by Sir William Rowan Hamilton and developed by P. G. Tait; it is of central importance in many three-dimensional physical problems. The symbol ∇ was originally named ‘nabla’ after a harp-like ancient Assyrian musical instrument of similar shape; it is now usual to adopt the term ‘del’ introduced by J. Willard Gibbs. In cartesian notation 4.1 $$ del = \nabla = i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z'}} $$ and may be applied as an operator either to a scalar or to a vector function of space. Again, treating the differentiators in ∇ as scalare, we may formally regard ∇ as a vector which can have either a scalar or a vector product with other vectors. In vector analysis there are three fundamental operations with ∇ which are of physical interest. If S is a scalar function and V a vector function of position, these operations are (i) ∇S, where ∇ acts as an operator; (ii) ∇. V, and (iii) ∇ × V, where ∇ is treated formally as a vector. Keywords: Angular Velocity; Scalar Field; Vector Analysis; Infinitesimal Element; Field Grad (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-5841-8_4 Ordering information: This item can be ordered from DOI: 10.1007/978-94-009-5841-8_4 Access Statistics for this chapter More chapters in Springer Books from Springer |
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