TeXipedia

delta

Represents a small change or variation in mathematics, particularly common in calculus and physics calculations.

Overview

Essential in mathematical notation for describing incremental changes, differences, and variations across multiple scientific domains.

  • Widely used in calculus to denote derivatives and small changes in variables
  • Fundamental in physics for expressing changes in physical quantities
  • Common in engineering for error analysis and tolerance calculations
  • Appears frequently in thermodynamics to represent changes in state variables
  • Used in statistics to indicate statistical differences or variations

Examples

Defining a small change or variation in a variable x.

Δx≈δx as δx→0\Delta x \approx \delta x \text{ as } \delta x \to 0 
\Delta x \approx \delta x \text{ as } \delta x \to 0

Using delta in a partial differential equation.

∂f∂x=lim⁡δx→0f(x+δx)−f(x)δx\frac{\partial f}{\partial x} = \lim_{\delta x \to 0} \frac{f(x + \delta x) - f(x)}{\delta x} 
\frac{\partial f}{\partial x} = \lim_{\delta x \to 0} \frac{f(x + \delta x) - f(x)}{\delta x}

Representing the Kronecker delta function.

δij={1if i=j0if i≠j\delta_{ij} = \begin{cases} 1 & \text{if } i = j \\ 0 & \text{if } i \neq j \end{cases} 
\delta_{ij} = \begin{cases} 1 & \text{if } i = j \\ 0 & \text{if } i \neq j \end{cases}