| 释义 |
nabla Math.|ˈnæblə|
[a. Gr. νάβλα: see nable (and cf. quot. 1879 s.v. nebel).]
= del.
The operator was introduced by Sir William Hamilton, who represented it by the symbol ◁. (In quot. 1837 he uses ∇′ as a symbol for any arbitrary function.)
[1837W. R. Hamilton in Trans. R. Irish Acad. XVII. 236 Considering x as a function ψ of a new variable o′ and performing any operation ∇′ with reference to the latter variable, ∇′fψ(o′) = ∇′ f(1 + Δ) (ψ(o′))o. 1846Proc. R. Irish Acad. III. 291 The following..general characteristic of operation i d / dx + j d / dy + k d / dz = ◁, in which x, y, z are ordinary rectangular coordinates, while i, j, k are his [sc. Hamilton's] own coordinate imaginary units, appears to him to be one of great importance in many researches. 1847W. R. Hamilton in Phil. Mag. XXXI. 291 In the paper designed for Southampton..the characteristic was written ∇; but this more common sign has been so often used with other meanings, that it seems desirable to abstain from appropriating it to the new signification here proposed. 1853― Lect. Quaternions vii. 610 Introducing, for abridgment, as a new characteristic of operation, a symbol defined by the formula ◁ = [etc.]. ]1884W. Thomson Notes Lect. Molecular Dynamics & Wave Theory of Light at Johns Hopkins Univ. x. 112 (MS.), I took the liberty of asking Professor Bell..whether he had a name for this symbol ∇2; and he has mentioned to me nabla, a humorous suggestion of Maxwell's. It is the name of an Egyptian harp, which was of that shape. 1892Phil. Trans. R. Soc. CLXXXIII. 431 Physical mathematics is very largely the mathematics of ∇. The name Nabla seems, therefore, ludicrously inefficient. 1939D. E. Rutherford Vector Methods iv. 50 A convenient method of writing grad ϕ is ∇ϕ, where ∇ (pronounced ‘nabla’) is defined as the vector operator ∇ ≡ i ∂ / ∂x + j ∂ / ∂y + k ∂ / ∂z . 1964[see del]. 1969L. Young Systems of Units in Electr. & Magn. v. 63 The symbol nabla, ∇, is a vector differential operator. |