December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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13.1 Separable Partial Differential Equations
INTRODUCTION
Partial differential equations (PDEs), like ordinary differential equations (ODEs), are classified as linear or nonlinear. Analogous to a linear ODE (see (6) of Section 1.1), the dependent variable and its partial derivatives appear only to the first power in a linear PDE. In this and the chapters that follow, we are concerned only with linear partial differential equations.
Linear Partial Differential Equation
If we let u denote the dependent variable and x and y the independent variables, then the general form of a linear second-order partial differential equation is given by
(1) ...
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