Definition:Differential Equation/Partial

Definition

A partial differential equation (abbreviated P.D.E. or PDE) is a differential equation which has:

one dependent variable

more than one independent variable.

The derivatives occurring in it are therefore partial.

Mixed Differential Equation

A mixed differential equation is a partial differential equation in which both ordinary derivatives and partial derivatives occur.

Also see

• Definition:Ordinary Differential Equation

Sources

• 1926: E.L. Ince: Ordinary Differential Equations ... (previous) ... (next): Chapter $\text I$: Introductory: $\S 1.1$ Definitions
• 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
• 1952: H.T.H. Piaggio: An Elementary Treatise on Differential Equations and their Applications (revised ed.) ... (previous) ... (next): Chapter $\text I$: Introduction and Definitions. Elimination. Graphical Representation: $3$. Definitions
• 1956: E.L. Ince: Integration of Ordinary Differential Equations (7th ed.) ... (previous) ... (next): Chapter $\text {I}$: Equations of the First Order and Degree: $1$. Definitions
• 1960: D.R. Bland: Vibrating Strings ... (next): Chapter $1$: Strings of Finite Length: $1.1$ Introduction
• 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $3$: The Differential Equation
• 1968: G. Stephenson: An Introduction to Partial Differential Equations for Science Students ... (next): Chapter $1$ Basic Concepts: $1.1$ Introduction
• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 1$: Introduction
• 1977: A.J.M. Spencer: Engineering Mathematics: Volume $\text { I }$ ... (previous) ... (next): Chapter $1$ Ordinary Differential Equations: $1.1$ Introduction: Classification of Differential Equations
• 1978: Garrett Birkhoff and Gian-Carlo Rota: Ordinary Differential Equations (3rd ed.) ... (previous) ... (next): Chapter $1$ First-Order Differential Equations: $1$ Introduction
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): differential equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): differential equation