Nabla
|
∇
|
|
|---|---|
| Mathematical signs | |
| arithmetic | |
| Plus sign | + |
| Minus sign | - , ./. |
| Mark | ⋅ , × |
| Divided sign | : , ÷ , / |
| Plus minus sign | ± , ∓ |
| Comparison sign | < , ≤ , = , ≥ , > |
| Root sign | √ |
| Percent sign | % |
| Analysis | |
| Sum symbol | Σ |
| Product mark | Π |
| Difference sign , Nabla | ∆ , ∇ |
| Prime | ′ |
| Partial differential | ∂ |
| Integral sign | ∫ |
| Concatenation characters | ∘ |
| Infinity symbol | ∞ |
| geometry | |
| Angle sign | ∠ , ∡ , ∢ , ∟ |
| Vertical , parallel | ⊥ , ∥ |
| Triangle , square | △ , □ |
| Diameter sign | ⌀ |
| Set theory | |
| Union , cut | ∪ , ∩ |
| Difference , complement | ∖ , ∁ |
| Element character | ∈ |
| Subset , superset | ⊂ , ⊆ , ⊇ , ⊃ |
| Empty set | ∅ |
| logic | |
| Follow arrow | ⇒ , ⇔ , ⇐ |
| Universal quantifier | ∀ |
| Existential quantifier | ∃ |
| Conjunction , disjunction | ∧ , ∨ |
| Negation sign | ¬ |
The symbol Nabla (∇) is a mathematical symbol that is mainly used in vector analysis to denote the Nabla operator . In addition, it is used in differential geometry to denote the relationship or the covariant derivative .
description
The symbol Nabla is not a letter, but arose from similar symbols of the quaternion analysis by William Rowan Hamilton . Peter Guthrie Tait introduced today's form of an upside-down delta Δ. The name "Nabla" comes from the theologian William Robertson Smith (1846-1894), who derived the form from the biblical lyre Nevel ( Hebrew נבל nével , ancient Greek νάβλα nábla , Latin nablium ).
The Nabla is identical to the symbol for water in the ancient four-element teaching . However, there is neither a substantive nor a historical relationship between the two symbols.
The character Nabla can be represented in HTML as ∇and in LaTeX as \nabla. In the Unicode character set, it has the symbol number 8711 ( hexadecimal 0x2207).
use
- In vector analysis , the Nabla operator is used for the vector representation of the differential operators for the gradient , the divergence and the rotation .
- In differential geometry , the symbol is used for affine relationships .
- In shipbuilding , Nabla symbolizes the structural displacement in cubic meters.
- In the APL programming language , the character starts and ends
∇the line editor for functions and, as a functional symbol, has the meaning of self-reference . Furthermore, the Nabla is part of some compound APL symbols such as⍒and⍫. - In microbiology / bioprocess engineering , Nabla denotes the sterility criterion .
Individual evidence
- ^ Manfredo Perdigão do Carmo: Riemannian Geometry. Birkhäuser, Boston 1992, ISBN 0-8176-3490-8 , p. 50.
- ↑ Capt. DRDerret, Dr. CBBarrass: Ship Stability for Masters and Mates Elsevier Butterworth-Heinemann, 5th Edition, ISBN 0-7506-4101-0 , p. 378.
- ↑ Dubasi Govardhana Rao: Introduction to Biochemical Engineering . Tata McGraw-Hill Education, 2010, ISBN 978-0-07-015138-3 ( google.de [accessed February 7, 2019]).