Definition:Differential Equation/Partial
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Definition
A partial differential equation 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 known as
The term partial differential equation is often presented in its abbreviated form PDE or P.D.E.
Examples
Also see
- Results about partial differential equations can be found here.
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