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Chapter 2 PARTIAL DIFFERENTIAL EQUATIONS OF SECOND …

Draft PDE Lecture Notes Khanday Department of Mathematics, University of Kashmir, Srinagar-190006 1 Chapter 2 PARTIAL DIFFERENTIAL EQUATIONS OF SECOND order INTRODUCTION: An equation is said to be of order two, if it involves at least one of the DIFFERENTIAL coefficients r = ( 2z / 2x), s = ( 2z / x y), t =( 2z / 2y), but now of higher order ; the quantities p and q may also enter into the equation. Thus the general form of a SECOND order PARTIAL DIFFERENTIAL equation is ( , , , , , , , ) =0 ..(1) The most general linear PARTIAL DIFFERENTIAL equation of order two in two independent variables x and y with variable coefficients is of the form + + + + + = ..(2) where , , , , , , are functions of and only and not all , , are zero.

PARTIAL DIFFERENTIAL EQUATIONS OF SECOND ORDER INTRODUCTION: An equation is said to be of order two, if it involves at least one of the differential coefficients r = (ò 2z / ò 2x), s = (ò 2z / ò x ò y), t = (ò 2z / ò 2y), but now of higher order; the quantities p and q may also enter into the equation. Thus the

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