Partial Differential Equation

Definition

A partial differential equation is an equation that relates a function of multiple variables to its partial derivatives. It involves the rates of change of the function with respect to each variable.

Analogy

Imagine you are baking a cake and you have different ingredients like flour, sugar, and eggs. The recipe for the cake is like a partial differential equation because it tells you how the final cake depends on the amounts of each ingredient and their interactions.

Related terms

Ordinary Differential Equation: An ordinary differential equation relates a function to its derivatives with respect to a single independent variable.

Boundary Conditions: Boundary conditions are additional equations or constraints that specify values or behaviors at the boundaries or edges of a system described by a partial differential equation.

Initial Conditions: Initial conditions are specific values or behaviors assigned to variables in a system described by a partial differential equation at an initial point in time or space.