∂

Not to be confused with 𝛿 or ð.

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 ${\frac {\partial z}{\partial x}}$ (read as "the partial derivative of z with respect to x"), the boundary operator in a chain complex, or the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold.

History

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. It represents a specialized cursive type of the letter d, just as 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, whose usage became widely adopted.

Names and coding

The symbol is variously referred to as "curly d", "rounded d", "curved d", "dabba", or "Jacobi's delta", or as "del" (but this name is also used for the "nabla" symbol ∇). It may also be pronounced simply "dee", "partial dee", "doh", or "die"

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

Uses

∂ is also used to denote the following:

• The Jacobian ${\frac {\partial (x,y,z)}{\partial (u,v,w)}}$.
• The boundary of a set in topology.
• The boundary operator on a chain complex in homological algebra.
• The boundary operator of a differential graded algebra.
• The conjugate of the Dolbeault operator on complex differential forms.

See also

• Differentiable programming
• Differential operator#Notations
• List of mathematical symbols
• 𝒹 (Unicode MATHEMATICAL SCRIPT SMALL D)
• ꝺ (lowercase d in Insular script)
• δ (lowercase Greek Delta)
• д (lowercase Cyrillic De, looks similar when italicized in some typefaces)