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First Order Partial Differential Equations, Part - 1 ...

First Order Partial Differential equations , Part - 1:Single linear and Quasilinear First Order EquationsPHOOLAN PRASADDEPARTMENT OF MATHEMATICSINDIAN INSTITUTE OF SCIENCE, BANGALORED efinitionFirst Order PDE in two independent variables is a relationF(x,y;u;ux,uy) = 0Fa knownrealfunction fromD3 R5 R(1)Examples: linear , semilinear, quasilinear, nonlinear equations -ux+uy= 0ux+uy=ku, candkare constantux+uy=u2uux+uy= 0u2x u2y= 0u2x+u2y+ 1 = 0ux+ 1 u2y= 0,defined for|uy| 1(2)A Model Lession FD PDE Part 1P. PrasadDepartment of Mathematics2 / 50 Symbols for various domains usedIn this lecture we denotebyDa domain inR2where a solution is defined,byD1a domain inR2where the coefficients of alinear equation are defined andbyD2is a domain in (x,y,u)-space ,R3finally byD3a domain inR5where the functionFof five independent variables is Model Lession FD PDE Part 1P.

De nition First order PDE in two independent variables is a relation F(x;y;u;u x;u y) = 0 Fa known real function from D 3 ˆR5!R (1) Examples: Linear, semilinear, quasilinear, nonlinear equations -

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