Basic Concepts and Definitions
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Partial Differential EquationsIntroductionBasic Concepts and Definitions
Definition of a Partial Differential Equation
Introduction
The definition of a partial differential equation begins with functions of several independent variables. In ordinary differential equations, the unknown function usually depends on one independent variable. In partial differential equations, the unknown function depends on two or more independent variables, and the equation contains one or more partial derivatives of that unknown function. We shall use this page to define the object carefully, introduce PDE notation, and explain what it means for a function to be a solution.
DEFINITION : Partial Differential Equation
A differential equation that contains, in addition to the dependent variable and the independent variables, one or more partial derivatives of the dependent variable is called a partial differential equation.
In general, a partial differential equation may be written in the form
Here are independent variables, is the dependent variable, and denote partial derivatives of .
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Dr. Bivash Majumder
Assistant Professor in Mathematics
Prabhat Kumar College, Contai
Definition of a Partial Differential Equation
The definition of a partial differential equation begins with functions of several independent variables. In ordinary differential equations, the unknown function usually depends on one independent variable. In partial differential equations, the unknown function depends on two or more independent variables, and the equation contains one or more partial derivatives of that unknown function. We shall use this page to define the object carefully, introduce PDE notation, and explain what it means for a function to be a solution.