Delta (Δ, δ) Definition

The uppercase Delta (Δ) is used for:

• Change of any changeable quantity, in mathematics and the sciences (more specifically, the difference operator); for example, in: ^{y₂ - y₁}⁄_{x2 - x1} = ^Δy⁄_Δx the average change of y per unit x (i.e. the change of y over the change of x). Delta is the initial letter of the Greek word diaphorá (διαφορά), "difference". (The small Latin letter d is used in much the same way for the notation of derivatives and differentials, which also describe change.)

• The Laplace operator.

• The discriminant of a polynomial equation, especially the quadratic equation: Δ = b² - 4ac

• The area of a triangle: Δ = ¹⁄₂absin C

• The symmetric difference of two sets.

• A macroscopic change in the value of a variable in mathematics or science.

• Uncertainty in a physical variable as seen in the uncertainty principle.

• An interval of possible values for a given quantity.

• Any of the delta particles in particle physics.

• The determinant of the matrix of coefficients of a set of linear equations (see Cramer's rule).

• That an associated locant number represents the location of a covalent bond in an organic compound, the position of which is variant between isomeric forms.

• A simplex, simplicial complex, or convex hull.

• In chemistry, the addition of heat in a reaction.

• In legal shorthand, it represents a defendant.

• In the financial markets, one of the Greeks, describing the rate of change of an option price for a given change in the underlying benchmark.

• A major seventh chord in jazz music notation.

• In genetics, it can stand for a gene deletion (e.g. the CCR5-Δ32, a 32 nucleotide/bp deletion within CCR5).

• The American Dental Association cites it (together with omicron for "odont") as the symbol of dentistry.

• The anonymous signature of James David Forbes.

• Determinacy (having a definite truth-value) in philosophical logic.

The lowercase Delta (δ) is used for:

• A change in the value of a variable in calculus.

• A Functional derivative in Functional calculus.

• An auxiliary function in calculus, used to rigorously define the limit or continuity of a given function.

• The Kronecker delta in mathematics.

• The degree of a vertex (graph theory).

• The Dirac delta function in mathematics.

• The transition function in automata.

• Deflection in engineering mechanics.

• The force of interest in actuarial science.

• The chemical shift of nuclear magnetic resonance in chemistry.

• The relative electronegativity of different atoms in a molecule, δ⁻ being more electronegative than δ⁺

• Text requiring deletion in proofreading; the usage is said to date back to classical times.

• In some of the manuscripts written by Dr. John Dee, the character of delta is used to represent Dee.

• A subunit of the F1 sector of the F-ATPase.

• The declination of an object in the equatorial coordinate system of astronomy.

• The dividend yield in the Black–Scholes option pricing formula.

• Ratios of environmental isotopes, such as ¹⁸O/¹⁶O and D/¹H from water are displayed using delta notation – δ¹⁸O and δD, respectively

• The rate of depreciation of the aggregate capital stock of an economy in an exogenous growth model in macroeconomics.

• In a system that exhibits electrical reactance, the angle between voltage and current.

• Partial charge in chemistry.

• The maximum birrefringence of a crystal in optical mineralogy.

The letters of the Ancient Greek Alphabet, which are frequently utilized in math and science:

• Greek Alphabet
• Greek Numerals

“Delta (Letter).” Wikipedia, Wikimedia Foundation, 6 Apr. 2020, en.wikipedia.org/wiki/Delta_(letter).