Open main menu

The character (Unicode: U+2202) is a stylized cursive d mainly used as a mathematical symbol. This symbol can be used variously to denote a partial derivative such as (read as "the partial derivative of z with respect to x")[1], the boundary operator in a chain complex, or the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold.

Contents

HistoryEdit

The symbol was originally introduced in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786.[2] It represents a specialized cursive type of the letter d, just like the integral sign originates as a specialized type of a long s (first used in print by Leibniz in 1686). Use of the symbol was discontinued by Legendre, but it was taken up again by Carl Gustav Jacob Jacobi in 1841,[3] whose usage became widely adopted.[4]

Names and codingEdit

The symbol is variously referred to "curly d", "rounded d", "curved d", or "Jacobi's delta",[4] or as "del"[5] (but this name is also used for the "nabla" symbol ). It may also be pronounced simply "dee",[6] or "partial dee".[7][8] "doh",[9] "die"[10] or "dabba".[11]

The Unicode character is accessed by HTML elements ∂ or ∂, the LaTeX symbol (Computer Modern glyph:  ) is accessed by \partial.

UsesEdit

is also used to denote the following:

See alsoEdit

ReferencesEdit

  1. ^ Christopher, Essex (2013). Calculus : a complete course. p. 682. ISBN 9780321781079. OCLC 872345701.
  2. ^ Adrien-Marie Legendre, "Memoire sur la manière de distinguer les maxima des minima dans le Calcul des Variations," Histoire de l'Academie Royale des Sciences (1786), pp. 7–37.
  3. ^ Carl Gustav Jacob Jacobi, "De determinantibus Functionalibus," Crelle's Journal 22 (1841), pp. 319–352.
  4. ^ a b "The 'curly d' was used in 1770 by Antoine-Nicolas Caritat, Marquis de Condorcet (1743-1794) in 'Memoire sur les Equations aux différence partielles,' which was published in Histoire de L'Academie Royale des Sciences, pp. 151-178, Annee M. DCCLXXIII (1773). On page 152, Condorcet says:
    Dans toute la suite de ce Memoire, dz & ∂z désigneront ou deux differences partielles de z, dont une par rapport a x, l'autre par rapport a y, ou bien dz sera une différentielle totale, & ∂z une difference partielle.
    However, the 'curly d' was first used in the form ∂u/∂x by Adrien Marie Legendre in 1786 in his 'Memoire sur la manière de distinguer les maxima des minima dans le Calcul des Variations,' Histoire de l'Academie Royale des Sciences, Annee M. DCCLXXXVI (1786), pp. 7-37, Paris, M. DCCXXXVIII (1788). On page 8, it reads:
    Pour éviter toute ambiguité, je répresentarie par ∂u/∂x le coefficient de x dans la différence de u, & par du/dx la différence complète de u divisée par dx.
    Legendre abandoned the symbol and it was re-introduced by Carl Gustav Jacob Jacobi in 1841. Jacobi used it extensively in his remarkable paper 'De determinantibus Functionalibus" Crelle’s Journal, Band 22, pp. 319-352, 1841 (pp. 393-438 of vol. 1 of the Collected Works).
    Sed quia uncorum accumulatio et legenti et scribenti molestior fieri solet, praetuli characteristica d differentialia vulgaria, differentialia autem partialia characteristica ∂ denotare.
    The 'curly d' symbol is sometimes called the 'rounded d' or 'curved d' or Jacobi’s delta. It corresponds to the cursive 'dey' (equivalent to our d) in the Cyrillic alphabet." Aldrich, John. "Earliest Uses of Symbols of Calculus". Retrieved 16 January 2014.
  5. ^ Bhardwaj, R.S. (2005), Mathematics for Economics & Business (2nd ed.), p. 6.4
  6. ^ Silverman, Richard A. (1989), Essential Calculus: With Applications, p. 216
  7. ^ Pemberton, Malcolm; Rau, Nicholas (2011), Mathematics for Economists: An Introductory Textbook, p. 271
  8. ^ Munem, Mustafa; Foulis, David (1978). Calculus with Analytic Geometry. New York, NY: Worth Publishers, Inc. p. 828. ISBN 0-87901-087-8.
  9. ^ Bowman, Elizabeth (2014), Video Lecture for University of Alabama in Huntsville
  10. ^ Christopher, Essex; Adams, Robert Alexander (2014). Calculus : a complete course (Eighth ed.). p. 682. ISBN 9780321781079. OCLC 872345701.
  11. ^ Gokhale, Mujumdar, Kulkarni, Singh, Atal, Engineering Mathematics I, p. 10.2, Nirali Prakashan ISBN 8190693549.