Basic Concepts and Definitions
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Partial Differential EquationsIntroductionBasic Concepts and Definitions
Linear, Quasi-linear, and Nonlinear Partial Differential Equations
Introduction
Linear quasi-linear and nonlinear partial differential equations form one of the first structural classifications in the subject. This classification depends on how the unknown function and its partial derivatives occur in the equation. We shall define these three types carefully and illustrate them through basic second-order examples.
DEFINITION : Linear Partial Differential Equation
A partial differential equation is called linear if it is linear in the unknown function and in all the partial derivatives of the unknown function, with coefficients depending only on the independent variables.
Thus, a linear partial differential equation contains no products, powers, or nonlinear functions of and its derivatives. For instance, terms such as , , , and do not occur in a linear partial differential equation.
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Author
Dr. Bivash Majumder
Assistant Professor in Mathematics
Prabhat Kumar College, Contai