TeXipedia

Delta

Represents a change or difference between two values in mathematics and science, particularly in calculus and physics.

Overview

Serves as a fundamental notation across multiple scientific disciplines, indicating the variation or increment between two states of a quantity.

  • Essential in calculus for expressing rates of change and finite differences
  • Common in physics for denoting changes in physical quantities like temperature, pressure, or energy
  • Used in mathematical proofs and theorems to represent the symmetric difference between sets
  • Appears frequently in engineering calculations for error analysis and tolerance specifications
  • Important in statistics for measuring variability and expressing confidence intervals

Examples

Change in a physical quantity, commonly used in physics and engineering.

ΔT=T2−T1\Delta T = T_2 - T_1 
\Delta T = T_2 - T_1

Discriminant in a quadratic equation.

Δ=b2−4ac\Delta = b^2 - 4ac 
\Delta = b^2 - 4ac

Laplace operator in vector calculus.

Δf=∂2f∂x2+∂2f∂y2\Delta f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} 
\Delta f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2}