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Second Order Linear Partial Differential Equations Part I

2008, 2012 Zachary S Tseng E 1 1 Second Order Linear Partial Differential Equations Part I Second Linear Partial Differential Equations ; Separation of Variables; 2 point boundary value problems; Eigenvalues and Eigenfunctions Introduction We are about to study a simple type of Partial Differential Equations (PDEs): the Second Order Linear PDEs. Recall that a Partial Differential equation is any Differential equation that contains two or more independent variables. Therefore the derivative(s) in the equation are Partial derivatives.

(Optional topic) Classification of Second Order Linear PDEs Consider the generic form of a second order linear partial differential equation in 2 variables with constant coefficients: a u xx + b u xy + c u yy + d u x + e u y + f u = g(x,y). For the equation to be of second order, a, b, and c cannot all be zero. Define

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